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All Textbook Solutions for Precalculus Enhanced with Graphing Utilities
In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C. y=| x |+2 D. y=-| x |+2 E. y= ( x-2 ) 2 F. y=- ( x+2 ) 2 G. y=| x-2 | H. y=-| x+2 | I. y=2 x 2 J. y=-2 x 2 K. y=2| x | L. y=-2| x |In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C. y=| x |+2 D. y=-| x |+2 E. y= ( x-2 ) 2 F. y=- ( x+2 ) 2 G. y=| x-2 | H. y=-| x+2 | I. y=2 x 2 J. y=-2 x 2 K. y=2| x | L. y=-2| x |In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C. y=| x |+2 D. y=-| x |+2 E. y= ( x-2 ) 2 F. y=- ( x+2 ) 2 G. y=| x-2 | H. y=-| x+2 | I. y=2 x 2 J. y=-2 x 2 K. y=2| x | L. y=-2| x |In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C. y=| x |+2 D. y=-| x |+2 E. y= ( x-2 ) 2 F. y=- ( x+2 ) 2 G. y=| x-2 | H. y=-| x+2 | I. y=2 x 2 J. y=-2 x 2 K. y=2| x | L. y=-2| x |In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C. y=| x |+2 D. y=-| x |+2 E. y= ( x-2 ) 2 F. y=- ( x+2 ) 2 G. y=| x-2 | H. y=-| x+2 | I. y=2 x 2 J. y=-2 x 2 K. y=2| x | L. y=-2| x |In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C. y=| x |+2 D. y=-| x |+2 E. y= ( x-2 ) 2 F. y=- ( x+2 ) 2 G. y=| x-2 | H. y=-| x+2 | I. y=2 x 2 J. y=-2 x 2 K. y=2| x | L. y=-2| x |In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C. y=| x |+2 D. y=-| x |+2 E. y= ( x-2 ) 2 F. y=- ( x+2 ) 2 G. y=| x-2 | H. y=-| x+2 | I. y=2 x 2 J. y=-2 x 2 K. y=2| x | L. y=-2| x |In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C. y=| x |+2 D. y=-| x |+2 E. y= ( x-2 ) 2 F. y=- ( x+2 ) 2 G. y=| x-2 | H. y=-| x+2 | I. y=2 x 2 J. y=-2 x 2 K. y=2| x | L. y=-2| x |In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C. y=| x |+2 D. y=-| x |+2 E. y= ( x-2 ) 2 F. y=- ( x+2 ) 2 G. y=| x-2 | H. y=-| x+2 | I. y=2 x 2 J. y=-2 x 2 K. y=2| x | L. y=-2| x |In problems 7-18, match each graph to one of the following functions: A. y= x 2 +2 B. y=- x 2 +2 C. y=| x |+2 D. y=-| x |+2 E. y= ( x-2 ) 2 F. y=- ( x+2 ) 2 G. y=| x-2 | H. y=-| x+2 | I. y=2 x 2 J. y=-2 x 2 K. y=2| x | L. y=-2| x |In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Shifted to the right 4 units.In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Shifted to the left 4 units.In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Shifted up 4 units.In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Shifted down 4 units.In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Reflected about the y-axis .In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Reflected about the x-axis .In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Vertically stretched by a factor of 4.In Problem 19-26, write the function whose graph is the graph of y= x 3 , but is: Horizontally stretched by a factor of 4.In Problem 27-30, find the function that is finally graphed after each of the following transformations is applied to the graph of y= x in the order stated. (1) Shift up 2 units (2) Reflect about the x-axis (3) Reflect about the y-axisIn Problem 27-30, find the function that is finally graphed after each of the following transformations is applied to the graph of y= x in the order stated. (1) Reflect about the x-axis (2) Shift right 3 units (3) Shift down 2 unitsIn Problem 27-30, find the function that is finally graphed after each of the following transformations is applied to the graph of y= x in the order stated. (1) Reflect about the x-axis (2) Shift up 2 units (3) Shift left 2 unitsIn Problem 27-30, find the function that is finally graphed after each of the following transformations is applied to the graph of y= x in the order stated. (1) Shift up 2 units (2) Reflect about the y-axis (3) Shift left 3 unitsIn Problem 27-30, find the function that is finally graphed after each of the following transformations is applied to the graph of y= x in the order stated. (1) Shift up 2 units (2) Reflect about the y-axis (3) Shift left 3 unitsIn Problem 27-30, find the function that is finally graphed after each of the following transformations is applied to the graph of y= x in the order stated. If ( 3,6 ) is a point on the graph of y=f( x ) , which of the following points must be on the graph of y=f( x ) ? a. ( 6,3 ) b. ( 6,-3 ) c. ( 3,-6 ) d. ( 3,6 )In Problem 27-30, find the function that is finally graphed after each of the following transformations is applied to the graph of y= x in the order stated. If ( 1,3 ) is a point on the graph of y=f( x ) , which of the following points must be on the graph of y=2f( x ) ? a. ( 1, 3 2 ) b. ( 2,3 ) c. ( 1,6 ) d. ( 1 2 ,3 )In Problem 27-30, find the function that is finally graphed after each of the following transformations is applied to the graph of y= x in the order stated. If ( 4,2 ) is a point on the graph of y=f( x ) , which of the following points must be on the graph of y=2f( x ) ? a. ( 4,1 ) b. ( 8,2 ) c. ( 2,2 ) d. ( 4,4 )In Problem 27-30, find the function that is finally graphed after each of the following transformations is applied to the graph of y= x in the order stated. Suppose that the x-intercepts of the graph of y=f( x ) are 5 and 3 . (a) What are the x-intercepts of the graph of y=f( x+2 ) ? (b) What are the x-intercepts of the graph of y=f( x-2 ) ? (c) What are the x-intercepts of the graph of y=4f( x ) ? (d) What are the x-intercepts of the graph of y=f( x ) ?In Problem 27-30, find the function that is finally graphed after each of the following transformations is applied to the graph of y= x in the order stated. Suppose that the x-intercepts of the graph of y=f( x ) are 8 and 1 . (a) What are the x-intercepts of the graph of y=f( x+4 ) ? (b) What are the x-intercepts of the graph of y=f( x-3 ) ? (c) What are the x-intercepts of the graph of y=2f( x ) ? (d) What are the x-intercepts of the graph of y=f( x ) ?Suppose that the function y=f( x ) is increasing on the interval [ 1,5 ] . (a) Over what interval is the graph of y=f( x+2 ) increasing? (b) Over what interval is the graph of y=f( x-5 ) increasing? (c) What can be said about the graph of y=-f( x ) ? (d) What can be said about the graph of y=f( x ) ?Suppose that the function y=f( x ) is decreasing on the interval [ 2,7 ] . (a) Over what interval is the graph of y=f( x+2 ) decreasing? (b) Over what interval is the graph of y=f( x-5 ) decreasing? (c) What can be said about the graph of y=-f( x ) ? (d) What can be said about the graph of y=f( x ) ?In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. f( x )= x 2 -1In Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. f( x )= x 2 +441AYU42AYU43AYUIn Problems 39-62, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Stan with the graph of the basic function (for example, y= x 2 ) and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. h( x )= x+145AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYU63AYU64AYU65AYU66AYU67AYU68AYUIn Problems 63-66, the graph of a function f is illustrated. Use the graph of f as the first step toward graphing each of the following functions: a. F( x )=f( x )+3 b. G( x )=f( x+2 ) c. P( x )=-f( x ) d. H( x )=f( x+1 )-2 e. Q( x )= 1 2 f( x ) f. g( x )=-f( x ) g. h( x )=f( 2x ) 63.In Problems 63-66, the graph of a function f is illustrated. Use the graph of f as the first step toward graphing each of the following functions: a. F( x )=f( x )+3 b. G( x )=f( x+2 ) c. P( x )=-f( x ) d. H( x )=f( x+1 )-2 e. Q( x )= 1 2 f( x ) f. g( x )=-f( x ) g. h( x )=f( 2x ) 64.71AYUIn Problems 63-66, the graph of a function f is illustrated. Use the graph of f as the first step toward graphing each of the following functions: a. F( x )=f( x )+3 b. G( x )=f( x+2 ) c. P( x )=-f( x ) d. H( x )=f( x+1 )-2 e. Q( x )= 1 2 f( x ) f. g( x )=-f( x ) g. h( x )=f( 2x ) 66.67. Using a graphing utility, graph f( x )= x 3 -9x for 4x4 . (a) Find the x-intercepts of the graph of f . (b) Approximate any local maxima and local minima. (c) Determine where f is increasing and where it is decreasing. (d) Without using a graphing utility, repeat parts (b)-(d) for y=f( x+2 ) . (e) Without using a graphing utility, repeat parts (b)-(d) for y=2f( x ) . (f) Without using a graphing utility, repeat parts (b)-(d) for y=f( x ) .Using a graphing utility, graph f( x )= x 3 -4x for 3x3 . (a) Find the x-intercepts of the graph of f . (b) Approximate any local maxima and local minima. (c) Determine where f is increasing and where it is decreasing. (d) Without using a graphing utility, repeat parts (b)-(d) for y=f( x-4 ) . (e) Without using a graphing utility, repeat parts (b)-(d) for y=f( 2x ) . (f) Without using a graphing utility, repeat parts (b)-(d) for y=-f( x ) .75AYU76AYU77AYU78AYU79AYU80AYU81AYU82AYU83AYU84AYU85AYU86AYU87AYU88AYU89AYU90AYU91AYU92AYU93AYU94AYU95AYU96AYU97AYU98AYU99AYU100AYU101AYU102AYU103AYU104AYU1. P=( x,y ) be a point on the graph of y= x 2 8 . (a) Express the distance d from P to the origin as a function of x. (b) What is d if x=0 ? (c) What is d if x=1 ? (d) Use a graphing utility to graph d=d( x ) . (e) For what values of x is d smallest?2. P=( x,y ) be a point on the graph of y= x 2 8 . (a) Express the distance d from P to the point ( 0,1 ) as a function of x. (b) What is d if x=0 ? (c) What is d if x=1 ? (d) Use a graphing utility to graph d=d( x ) . (e) For what values of x is d smallest?3. P=( x,y ) be a point on the graph of y= x . (a) Express the distance d from P to the point ( 1,0 ) as a function of x. (b) Use a graphing utility to graph d=d( x ) . (c) For what values of x is d smallest?4. P=( x,y ) be a point on the graph of y= 1 x . (a) Express the distance d from P to the origin as a function of x. (b) Use a graphing utility to graph d=d( x ) . (c) For what values of x is d smallest?5. A right triangle has one vertex on the graph of y= x 3 , x0 , at ( x,y ) , another at the origin, and the third on the positive y-axis at ( 0,y ) , as shown in the figure. Express the area A of the triangle as a function of x.6. A right triangle has one vertex on the graph of y=9 x 2 , x0 , at ( x,y ) , another at the origin, and the third on the positive x-axis at ( x,0 ) . Express the area A of the triangle as a function of x.7. A rectangle has one corner in quadrant I on the graph of y=16 x 2 , another at the origin, a third on the positive y-axis , and the fourth on the positive x-axis . See the figure below. Express the area A of the rectangle as a function of x. What is the domain of A? Graph A=A( x ) . For what value of x is A largest?8. A rectangle is inscribed in a semicircle of radius 2. See the figure. Let P=( x,y ) be the point in quadrant I that is a vertex of the rectangle and is on the circle. (a) Express the area A of the rectangle as a function of x. (b) Express the perimeter p of the rectangle as a function of x. (c) Graph A=A( x ) . For what value of x is A largest? (d) Graph P=P( x ) . For what value of x is p largest?9. A rectangle is inscribed in a semicircle of radius 2. See the figure. Let P=( x,y ) be the point in quadrant I that is a vertex of the rectangle and is on the circle. (a) Express the area A of the rectangle as a function of x. (b) Express the perimeter p of the rectangle as a function of x. (c) Graph A=A( x ) . For what value of x is A largest? (d) Graph P=P( x ) . For what value of x is p largest?10. A circle of radius r is inscribed in a square. see the figure. (a) Express the area A of the square as a function of the radius r of the circle. (b) Express the perimeter p of the square as a function of r.11. Geometry A wire 10 meters long is to be cut into two pieces. One piece will be shaped as a square, and the other piece will be shaped as a circle. See the figure. (a) Express the total area A enclosed by the pieces of wire as a function of the length x of a side of the square. (b) What is the domain of A? (c) Graph A=A( x ) . For what value of x is A smallest?12AYU13. Geometry A wire of length x is bent into the shape of a circle. (a) Express the circumference C of the circle as a function of x. (b) Express the area A of the circle as a function of x.14AYU15. Geometry A semicircle of radius r is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle. See the figure (a) Express the area A of the rectangle as a function of the radius r of the semicircle. (b) Express the perimeter p of the rectangle as a function of r.16. Geometry An equilateral triangle is inscribed in a circle of radius r. See the figure. Express the circumference C of the circle as a function of the length x of a side of the triangle. [Hint: First show that r 2 = x 2 3 .]17AYU18AYU19AYU20AYU21AYU22. Installing Cable TV MetroMedia Cable is asked to provide service to a customer whose house is located 2 miles from the road along which the cable is buried. The nearest connection box for the cable is located 5 miles down the road. See the figure. (a) If the installation cost is S500 per mile along the road and 700 per mile off the road, build a model that expresses the total cost C of installation as a function of the distance x (in miles) from the connection box to the point where the cable installation turns off the road. Find the domain of C=C( x ) . (b) Compute the cost if x=1 mile. (c) Compute the cost if x=3 miles. (d) Graph the function C=C( x ) . Use TRACE to see how the cost C varies as x changes from 0 to 5. (e) What value of x results in the least cost?23. Time Required to Go from an Island to a Town An island is 2 miles from the nearest point P on a straight shoreline. A town is 12 miles down the shore from P. See the illustration. (a) If a person can row a boat at an average speed of 3 miles per hour and the same person can walk 5 miles per hour, build a model that expresses the time T that it takes to go from the island to town as a function of the distance X from P to where the person lands the boat. (b) What is the domain of Τ? (c) How long will it take to travel from the island to town if the person lands the boat 4 miles from P? (d) How long will it take if the person lands the boat 8 miles from Ρ?24. Filling a Conical Tank Water is poured into a container in the shape of a right circular cone with radius 4 feet and height 16 feet. See the figure. Express the volume V of the water in the cone as a function of the height h of the water. [Hint: The volume V of a cone of radius r and height h is V= 1 3 r 2 h .]25AYU26. Constructing an Open Box An open box with a square base is required to have a volume of 10 cubic feet. (a) Express the amount A of material used to make such a box as a function of the length x of a side of the square base. (b) How much material is required for a base 1 foot by 1 foot? (c) How much material is required for a base 2 feet by 2 feet? (d) Use a graphing utility to graph A=A( x ) . For what value of x is A smallest?In Problems 1-3: (a) Determine the slope and y-intercept of each linear function. (b) Find the average rate of change of each function. (c) Graph each function. Label the intercepts. (d) Determine whether the function is increasing, decreasing, or constant. 1. f( x )=2x5In Problems 1-3: (a) Determine the slope and y-intercept of each linear function. (b) Find the average rate of change of each function. (c) Graph each function. Label the intercepts. (d) Determine whether the function is increasing, decreasing, or constant. 2. F( x )= 1 3 x+1In Problems 1-3: (a) Determine the slope and y-intercept of each linear function. (b) Find the average rate of change of each function. (c) Graph each function. Label the intercepts. (d) Determine whether the function is increasing, decreasing, or constant. 3. G(x)=4In Problems 4 and 5, determine whether the function is linear or nonlinear. If the function is linear, find the equation of the line. 4.In Problems 4 and 5, determine whether the function is linear or nonlinear. If the function is linear, find the equation of the line. 5.In Problems 6-8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting). 6. f( x )= (x2) 2 +2In Problems 6-8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting). 7. f( x )= ( x4 ) 2In Problems 6-8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting). 8. f( x )=2 (x+1) 2 +4In Problems 9-14, (a) graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. 9. f( x )= x 2 4x+6In Problems 9-14, (a) graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. 10. f( x )= 1 2 x 2 +2In Problems 9-14, (a) graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. 11. f( x )=4 x 2 +4xIn Problems 9-14, (a) graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. 12. f(x)=9 x 2 +6x+1In Problems 9-14, (a) graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. 13. f(x)= x 2 +x+ 1 2In Problems 9-14, (a) graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. 14. f( x )=3 x 2 +4x1In Problems 15-17, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value. 15. f( x )=3 x 2 6x+4In Problems 15-17, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value. 16. f(x)= x 2 +8x4In Problems 15-17, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value. 17. f( x )=2 x 2 +4In Problems 18-19, solve each quadratic inequality. 18. x 2 +6x160In Problems 18-19, solve each quadratic inequality. 19. 3 x 2 14x+520. In Problems 20 and 21, find the quadratic function for which: Vertex is (1,2) ; contains the point ( 1,6 )21. In Problems 20 and 21, find the quadratic function for which: Contains the points ( 0,5 ) , ( 1,2 ) , and ( 3,2 )22. Sales Commissions Bill has just been offered a sales position for a computer company. His salary would be 25,000 per year plus 1 of his total annual sales. (a) Find a linear function that relates Bill's annual salary. S, to his total annual sales, x. (b) If Bill’s total annual sales were 1,000,000 , what would be Bill’s salary? (c) What would Bill have to sell to ear 1,000,000 ? (d) Determine the sales required of Bill for his salary to exceed 150,000 .23. Demand Equation the price p (in dollars) and the quantity x sold of a certain product obey the demand equation p= 1 10 x+150 0x1500 (a) Express the revenue R as a function of x. (b) What is the revenue if 100 units are sold? (c) What quantity x maximizes revenue? What is the maximum revenue? (d) What price should the company charge to maximize revenue?24. Enclosing the Most Area with a Fence A farmer with 10,000 meters of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. See the figure. What is the largest area that can be enclosed?25. Minimizing Marginal Cost Callaway Golf Company has determined that the marginal cost C of manufacturing x Big Bertha golf clubs may be expressed by the quadratic function C(x)=4.9 x 2 617.4x+19,600 (a) How many clubs should be manufactured to minimize the marginal cost? (b) At this level of production, what is the marginal cost?26. Maximizing Area A rectangle has one vertex on the line y=10x . x0 , another at the origin, one on the positive x-axis , and one on the positive y-axis . Express the area A of the rectangle as a function of x. Find the largest area A that can he enclosed by the rectangle.27. Parabolic Arch Bridge A horizontal bridge is in the shape of a parabolic arch. Given the information shown in the figure, what is the height h of the arch 2 feet from shore?28. Bono Length Research performed at NASA, led by Dr. Emily R. Morey-Holton, measured the lengths of the right humerus and right tibia in 11 rats that were sent to space on Spacelab Life Sciences 2. The following data were collected. (a) Draw a scatter diagram of the data treating length of the right humerus as the independent variable. (b) Based on the scatter diagram, do you think that there is a linear relation between the length of the right humerus and the length of the right tibia? (c) Use a graphing utility to find the line of best fit relating length of the right humerus and length of the right tibia. (d) Predict the length of the right tibia on a rat whose right humerus is 26.5 millimeters (mm).29. Advertising A small manufacturing firm collected the following data on advertising expenditures A (in thousands of dollars) and total revenue R (in thousands of dollars). (a) Draw a scatter diagram of the data. Comment on the type of relation that may exist between the two variables. (b) The quadratic function of best fit to these data is R(A)=7.76 A 2 +411.88A+942.72 Use this function to determine the optimal level of advertising. (c) Use the function to predict the total revenue when the optimal level of advertising is spent. (d) Use a graphing utility to verify that the function given in part (b) is the quadratic function of best fit. (e) Use a graphing utility to draw a scatter diagram of the data and then graph the quadratic function of best fit on the scatter diagram.For the linear function f( x )=4x+3 , a. Find the slope and y-intercept . b. Determine whether f is increasing, decreasing, or constant. c. Graph f .Determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.Graph f(x)= (x3) 2 2 using transformations.In Problems 4 and 5, a. Determine whether the graph opens up or down. b. Determine the vertex of the graph of the quadratic function. c. Determine the axis of symmetry of the graph of the quadratic function. d. Determine the intercepts of the graph of the quadratic function. e. Use the information in parts (a)-(d) to graph the quadratic function. f. Based on the graph, determine the domain and the range of the quadratic function. g. Based on the graph, determine where the function is increasing and where it is decreasing. f(x)=3 x 2 12x+4In Problems 4 and 5, a. Determine whether the graph opens up or down. b. Determine the vertex of the graph of the quadratic function. c. Determine the axis of symmetry of the graph of the quadratic function. d. Determine the intercepts of the graph of the quadratic function. e. Use the information in parts (a)-(d) to graph the quadratic function. f. Based on the graph, determine the domain and the range of the quadratic function. g. Based on the graph, determine where the function is increasing and where it is decreasing. g(x)=2 x 2 +4x5Determine the quadratic function for the given graph.Determine whether f( x )=-2 x 2 +12x+3 has a maximum or minimum value. Then find the maximum or minimum value.Solve, x 2 10x+240 .The weekly rental cost of a 20-foot recreational vehicle is 129.50 plus 0.15 per mile. a. Find a linear function that expresses the cost C as a function of miles driven m . b. What is the rental cost if 860 miles are driven? c. How many miles were driven if the rental cost is 213.80 ?The price p (in dollars) and the quantity x sold of a certain product obey the demand equation p= 1 10 x+1000 . a. Find a model that expresses the revenue R as a function of x . b. What is the revenue if 400 units are sold? c. What quantity x maximizes revenue? What is the maximum revenue? d. What price should the company charge to maximize revenue?Consider these two data sets: One data set follows a linear pattern and one data set follows a quadratic relation. a. Draw a scatter diagram of each data set. Determine which is linear and which is quadratic. For the linear data, indicate whether the relation shows a positive or negative slope. For the quadratic relation, indicate whether the quadratic function of best fit will open up or down. b. For the linear data set, find the line of best fit. c. For the quadratic data set, find the quadratic function of best fit.Find the distance between the points P=( 1,3 ) and Q=( 4,2 ) . Find the midpoint of the line segment from P to Q .Which of the following points are on the graph of, y= x 3 3x+1 ? a. ( 2,1 ) b. ( 2,3 ) c. ( 3,1 )Solve the inequality 5x+30 and graph the solution set.Find the equation of the line containing the points ( 1,4 ) and ( 2,2 ) . Express your answer in slope-intercept form and graph the line.Find the equation of the line perpendicular to the line y=2x+1 and containing the point ( 3,5 ) . Express your answer in slope-intercept form and graph the line.Graph the equation x 2 + y 2 4x+8y5=0 .Does the following relation represent a function? { ( 3,8 ),( 1,3 ),( 2,5 ),( 3,8 ) }For the function f defined by f( x )= x 2 4x+1 , find: a. f( 2 ) b. f( x )+f( 2 ) c. f( x ) d. f( x ) e. f(x+2) f. f( x+h )f( x ) h h0Find the domain of h(z)= 3z1 6z7 .Is the following graph the graph of a function?Consider the function f(x)= x x+4 . a. Is the point (1, 1 4 ) on the graph of f ? b. If x=2 , what is f(x) ? What point is on the graph of f ? c. If f( x )=2 , what is x ? What point is on the graph of f ?Is the function f(x)= x 2 2x+1 even, odd, or neither?Approximate the local maximum values and local minimum values of f( x )= x 2 5x+1 on [4,4] . Determine where the function is increasing and where it is decreasing.If f(x)=3x+5 and g(x)=2x+1 , a. Solve f(x)=g( x ) . b. Solve f(x)g(x) .For the graph of the function f , a. Find the domain and the range of f . b. Find the intercepts. c. Is the graph of f symmetric with respect to the x-axis , the y-axis , or the origin? d. Find f( 2 ) . e. For what value(s) of x is f( x )=3 ? f. Solve f( x )0 . g. Graph y=f( x )+2 . h. Graph y=f(x) . i. Graph y=2f( x ) . j. Is f even, odd, or neither? k. Find the interval(s) on which f is increasing.Graph y=2x3 . (pp. 32-35)Find the slope of the line joining the points ( 2,5 ) and ( 1,3 ) . (pp. 30-31)Find the average rate of change of f(x)=3 x 2 2 , from 2 to 4. (pp. 88-89)Solve: 6x900=15x+2850 . (pp. A44-A46)If f( x )= x 2 4 , find f( 2 ) . (pp. 60-62)True or False The graph of the function f( x )= x 2 is increasing on the interval [0,) . (p. 84)For the graph of the linear function f( x )=mx+b , m is the _____ and b is the_____.If the slope m of the graph of a linear function is _____, the function is increasing over its domain.True or False The slope of a nonvertical line is the average rate of change of the linear function.True or False The average rate of change of f( x )=2x+8 is 8.What is the only type of function that has a constant average rate of change? a. linear function b. quadratic function c. step function d. absolute value functionA car has 12,500 miles on its odometer. Say the car is driven an average of 40 miles per day. Choose the model that expresses the number of miles N that will be on its odometer after x days. a. N( x )=40x+12,500 b. N( x )=40x12,500 c. N( x )=12,500x+40 d. N( x )=40x+12,500In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. f(x)=2x+3In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. g( x )=5x4In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. h( x )=3x+4In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. p(x)=x+6In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. f(x)=x3In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. h( x )=x+4In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. F(x)=4In Problems 13-20, a linear function is given. a. Determine the slope and y-intercept of each Junction. b. Use the slope and y-intercept to graph the linear function. c. Determine the average rate of change of each function. d. Determine whether the linear function is increasing, decreasing, or constant. G(x)=2In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.Suppose that f( x )=4x1 and g(x)=2x+5 . a. Solve f( x )=0 . b. Solve f( x )0 . c. Solve f(x)=g( x ) . d. Solve f( x )g(x) . e. Graph y=f( x ) and y=g( x ) and label the point that represents the solution to the equation f( x )=g(x) .Suppose that f( x )=3x+5 and g(x)=2x+15 . a. Solve f( x )=0 . b. Solve f( x )0 . c. Solve f(x)=g( x ) . d. Solve f( x )g(x) . e. Graph y=f( x ) and y=g( x ) and label the point that represents the solution to the equation f( x )=g(x) .In parts (a) - (f), use the following figure. a. Solve f( x )=50 . b Solve f( x )=80 . c. Solve f( x )=0 . d. Solve f( x )50 . c. Solve f( x )80 . f. Solve 0f( x )80 .In parts (a) - (f), use the following figure. a. Solve g( x )=20 . b Solve g( x )=60 . c. Solve g( x )=0 . d. Solve g( x )20 . c. Solve g( x )60 . f. Solve 0g( x )60 .In parts (a) and (b), use the following figure. a. Solve the equation: f( x )=g( x ) . b. Solve the inequality: f( x )g( x ) .In parts (a) and (b), use the following figure. a. Solve the equation: f( x )=g( x ) . b. Solve the inequality: f( x )g( x ) .In parts (a) and (b), use the following figure. a. Solve the equation: f( x )=g( x ) . b. Solve the inequality: g( x )f( x )h( x ) .In parts (a) and (b), use the following figure. a. Solve the equation: f( x )=g( x ) . b. Solve the inequality: g( x )f( x )h( x ) .Car Rentals The cost C , in dollars, of a one-day car rental is modeled by the function C( x )=0.35x+45 , where x is the number of miles driven. a. What is the cost if you drive x=40 miles? b. If the cost of renting the car is 108 , how many miles did you drive? c. Suppose that you want the cost to be no more than 150 . What is the maximum number of miles that you can drive? d. What is the implied domain of C ? e. Interpret the slope. f. Interpret the y-intercept .Phone Charges The monthly cost C , in dollars, for calls from the United States to Japan on a certain phone plan is modeled by the function C( x )=0.24x+5 , where x is the number of minutes used. a. What is the cost if you talk on the phone for x=50 minutes? b. Suppose that your monthly bill is 20.36 . How many minutes did you use the phone? c. Suppose that you budget yourself 40 per month for the phone. What is the maximum number of minutes that you can talk? d. What is the implied domain of C if there are 30 days in the month? e. Interpret the slope. f. Interpret the y-intercept .Supply and Demand Suppose that the quantity supplied S and the quantity demanded D of T-shirts at a concert are given by the following functions: S( p )=600+50p D( p )=120025p where p is the price of a T-shirt. a. Find the equilibrium price for T-shirts at this concert. What is the equilibrium quantity? b. Determine the prices for which quantity demanded is greater than quantity supplied. c. What do you think will eventually happen to the price of T-shirts if quantity demanded is greater than quantity supplied?Supply and Demand Suppose that the quantity supplied S and the quantity demanded D of hot dogs at a baseball game are given by the following functions: S( p )=2000+3000p D( p )=10,0001000p where p is the price of a hot dog. a. Find the equilibrium price for hot dogs at the baseball game. What is the equilibrium quantity? b. Determine the prices for which quantity demanded is less than quantity supplied. c. What do you think will eventually happen to the price of hot dogs if quantity demanded is less than quantity supplied?Taxes The function T( x )=0.15(x9225)+922.50 represents the tax bill T of a single person whose adjusted gross income is x dollars for income between 9225 and 37,450 , inclusive, in 2015. Source: Internal Revenue Service a. What is the domain of this linear function? b. What is a single filer's tax bill if adjusted gross income is 20,000 ? c. Which variable is independent and which is dependent? d. Graph the linear function over the domain specified in part (a). e. What is a single filer’s adjusted gross income if the tax bill is 3663.75 ? f. Interpret the slope.Competitive Balance Tax In 2011, major league baseball signed a labor agreement with the players. In this agreement, any team whose payroll exceeded 189 million in 2015 had to pay a competitive balance tax of 50% (for four or more consecutive offenses). The linear function T( p )=0.50( p189 ) describes the competitive balance tax T of a team whose payroll was p (in millions of dollars). Source: Major League Baseball a. What is the implied domain of this linear function? b. What was the competitive balance tax for the New York Yankees whose 2015 payroll was 214.2 million? c. Graph the linear function. d. What was the payroll of a team that paid a competitive balance tax of 15.7 million? e. Interpret the slope.The point at which a company’s profits equal zero is called the company’s break-even point. For Problems 43 and 44, let R represent a company’s revenue, let C represent the company’s costs, and let x represent the number of units produced and sold each day. a. Find the firm’s break-even point; that is, find x so that R=C . b. Find the values of x such that R( x )C( x ) . This represents the number of units that the company must sell to earn a profit. R( x )=8x C( x )=4.5x+17,500The point at which a company’s profits equal zero is called the company’s break-even point. For Problems 43 and 44, let R represent a company’s revenue, let C represent the company’s costs, and let x represent the number of units produced and sold each day. a. Find the firm’s break-even point; that is, find x so that R=C . b. Find the values of x such that R( x )C( x ) . This represents the number of units that the company must sell to earn a profit. R( x )=12x C( x )=10x+15,000Straight-line Depreciation Suppose that a company has just purchased a new computer for 3000 . The company chooses to depreciate the computer using the straight-line method over 3 years. a. Write a linear model that expresses the book value V of the computer as a function of its age x . b. What is the implied domain of the function found in part (a)? c. Graph the linear function. d. What is the book value of the computer after 2 years? e. When will the computer have a book value of 2000 ?Straight-line Depreciation Suppose that a company has just purchased a new machine for its manufacturing facility for 120,000 . The company chooses to depreciate the machine using the straight-line method over 10 years. a. Write a linear model that expresses the book value V of the machine as a function of its age x . b. What is the implied domain of the function found in part (a)? c. Graph the linear function. d. What is the book value of the machine after 4 years? e. When will the machine have a book value of 72,000 ?Cost Function The simplest cost function is the linear cost function, C(x)=mx+b , where the y-intercept b represents the fixed costs of operating a business and the slope m represents the cost of each item produced. Suppose that a small bicycle manufacturer has daily fixed costs of 90 , and each bicycle costs 2000 to manufacture. a. Write a linear model that expresses the cost C of manufacturing x bicycles in a day. b. Graph the model. c. What is the cost of manufacturing 14 bicycles in a day? d. How many bicycles could be manufactured for 3780 ?Cost Function Refer to Problem 47. Suppose that the landlord of the building increases the bicycle manufacturer's rent by 100 per month. a. Assuming that the manufacturer is open for business 20 days per month, what are the new daily fixed costs? b. Write a linear model that expresses the cost C of manufacturing x bicycles in a day with the higher rent. c. Graph the model. d. What is the cost of manufacturing 14 bicycles in a day? e. How many bicycles can be manufactured for 3780 ?Truck Rentals A truck rental company rents a truck for one day by charging 39.95 plus 0.89 per mile. a. Write a linear model that relates the cost C , in dollars, of renting the truck to the number x of miles driven. b. What is the cost of renting the truck if the truck is driven 110 miles? 230 miles?International Calling A cell phone company offers an international plan by charging 30 for the first 80 minutes, plus 0.50 for each minute over 80. a. Write a linear model that relates the cost C , in dollars, of talking x minutes, assuming x80 . b. What is the cost of talking 105 minutes? 120 minutes?Developing a Linear Model from Data How many songs can an iPod hold? The following data represent the memory m and the number of songs n . a. Plot the ordered pairs (m,n) in a Cartesian plane. b. Show that the number of songs n is a linear function of memory m . c. Determine the linear function that describes the relation between m and n . d. What is the implied domain of the linear function? e. Graph the linear function in the Cartesian plane drawn in part (a). f. Interpret the slope.Developing a Linear Model from Data The following data represent the various combinations of soda and hot dogs that Yolanda can buy at a baseball game with 60 . a. Plot the ordered pairs (s,h) in a Cartesian plane. b. Show that the number of hot dogs purchased h is a linear function of the number of sodas purchased s . c. Determine the linear function that describes the relation between s and h . d. What is the implied domain of the linear function? e. Graph the linear function in the Cartesian plane drawn in part (a). f. Interpret the slope. g. Interpret the values of the intercepts.Which of the following functions might have the graph shown? (More than one answer is possible). a. f( x )=2x7 b. g(x)=3x+4 c. H( x )=5 d. F(x)=3x+4 e. G( x )=x+2Which of the following functions might have the graph shown? More than one answer is possible). a. f( x )=3x+1 b. g( x )=2x+3 c. H( x )=3 d. F( x )=4x1 e. G(x)= 2 3 x+3Under what circumstances is a linear function f( x )=mx+b odd? Can a linear function ever be even?Explain how the graph of f( x )=mx+b can be used to solve mx+b0 .Plot the points ( 1,5 ),( 2,6 ),( 3,9 ),( 1,12 ) in the Cartesian plane. Is the relation { ( 1,5 ),( 2,6 ),( 3,9 ),( 1,12 ) } a function? Why? (pp. 2 and 57-60)Find an equation of the line containing the points ( 1,4 ) and ( 3,8 ) . (pp. 35-36)A _____________ is used to help us to see what type of relation, if any, may exist between two variables.If the Independent variable in a line of best fit y=0.008x+14 is credit score, and the dependent variable is the interest rate on a used-car loan, then the slope is interpreted as follows: If credit score increases by 1 point, the interest rate will __________ (increase/decrease) by ________ percent, on average.In Problems 5-10, examine the scatter diagram and determine whether the type of relation is linear or nonlinear.In Problems 5-10, examine the scatter diagram and determine whether the type of relation is linear or nonlinear.In Problems 5-10, examine the scatter diagram and determine whether the type of relation is linear or nonlinear.In Problems 5-10, examine the scatter diagram and determine whether the type of relation is linear or nonlinear.In Problems 5-10, examine the scatter diagram and determine whether the type of relation is linear or nonlinear.In Problems 5-10, examine the scatter diagram and determine whether the type of relation is linear or nonlinear.In Problems 11-16, (a) Draw a scatter diagram. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Use a graphing utility to find the line of best fit. (e) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.In Problems 11-16, (a) Draw a scatter diagram. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Use a graphing utility to find the line of best fit. (e) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.In Problems 11-16, (a) Draw a scatter diagram. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Use a graphing utility to find the line of best fit. (e) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.In Problems 11-16, (a) Draw a scatter diagram. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Use a graphing utility to find the line of best fit. (e) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.In Problems 11-16, (a) Draw a scatter diagram. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Use a graphing utility to find the line of best fit. (e) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.In Problems 11-16, (a) Draw a scatter diagram. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Use a graphing utility to find the line of best fit. (e) Use a graphing utility to draw the scatter diagram and graph the line of best fit on it.17AYU18AYU19AYU20AYU21AYU22AYU23AYU24AYU25AYUList the intercepts of the equation y= x 2 9 . (pp. 18-19)2AYUTo complete the square of x 2 5x , you add the number ______. (p. A49)To graph y= (x4) 2 you shift the graph of y= x 2 to the _______ a distance of ________ units. (pp. 106-108)The graph of a quadratic function is called a(n) ____________.The vertical line passing through the vertex of a parabola is called the ________________.The x-coordinate of the vertex of f( x )=a x 2 +bx+c,a0 , is ______.True or False The graph of f( x )=2 x 2 +3x4 opens up.True or False The y-coordinate of the vertex of f( x )= x 2 +4x+5 is f( 2 ) .True or False If the discriminant b 2 4ac=0 , the graph of f( x )=a x 2 +bx+c,a0 , will touch the x-axis at its vertex.If b 2 4ac0 , which of the following conclusions can be made about the graph of f(x)=a x 2 +bx+c,a0 ? (a) The graph has two distinct x-intercepts . (b) The graph has no x-intercepts . (c) The graph has three distinct x-intercepts . (d) The graph has one x-intercepts .If the graph of f( x )=a x 2 +bx+c,a0 , has a maximum value at its vertex, which of the following conditions must be true? (a) b 2a 0 (b) b 2a 0 (c) a0 (d) a0In Problems 13-20, match each graph to one the following functions. f( x )= x 2 1In Problems 13-20, match each graph to one the following functions. f(x)= x 2 1In Problems 13-20, match each graph to one the following functions. f(x)= x 2 2x+1In Problems 13-20, match each graph to one the following functions. f( x )= x 2 +2x+1In Problems 13-20, match each graph to one the following functions. f( x )= x 2 2x+2In Problems 13-20, match each graph to one the following functions. f( x )= x 2 +2xIn Problems 13-20, match each graph to one the following functions. f( x )= x 2 2xIn Problems 13-20, match each graph to one the following functions. f( x )= x 2 +2x+2In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )= 1 4 x 2In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )=2 x 2 +4In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f(x)= (x+2) 2 2In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )= (x3) 2 10In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f(x)= x 2 +4x+2In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )= x 2 6x1In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )=2 x 2 4x+1In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f(x)=3 x 2 +6xIn Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f(x)= x 2 2xIn Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )=2 x 2 +6x+2In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f( x )= x 2 +x1In Problems 21-32, graph the function f by starting with the graph of y= x 2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility. [Hint: If necessary, write f in the form f( x )=a (xh) 2 +k .] f(x)=2/3 x 2 +4/3x1In Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )= x 2 +2xIn Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f(x)= x 2 4xIn Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )= x 2 6xIn Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f(x)= x 2 +4xIn Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f(x)= x 2 +2x8In Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )= x 2 2x3In Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )= x 2 +2x+1In Problems 33-48, (a) graph each quadratic function by determining whether it graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )= x 2 +6x+9In Problems 33-48, (a) graph each quadratic function by determining whether Us graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )=2 x 2 x+2In Problems 33-48, (a) graph each quadratic function by determining whether Us graph opens up or down and by finding its vertex, axis of symmetry, y-intercept,andx-intercepts , if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. Verify your results using a graphing utility. f( x )=4 x 2 2x+1