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All Textbook Solutions for Precalculus

120RE 121RE 1T Given x=y4, a. Determine the x-andy-intercepts of the graph of the equation. b. Does the equation define y as a function of x?3T For Exercises 4-5, determine if the relation defines y as a function of x.For Exercises 4-5, determine if the relation defines y as a function of x.Given fx=2x2+7x3, find a.f1. b.fx+h. c. The difference quotient: fx+hfxh . d. The x-intercepts of the graph of f . e. The y-intercepts of the graph of f . f. The average rate of change of f on the interval 1,3.7T For Exercises 8-9, write the domain in interval notation. fw=2w3w+7 For Exercises 8-9, write the domain in interval notation. fc=4c Given 3x=4y+8, a. Identify the slope. b. Identify the y-intercept. c. Graph the line. d. What is the slope of a line perpendicular to this line? e. What is the slope of a line parallel to this line?Write an equation of the line passing through the point 2,6 and perpendicular to the defined by x+3y=4.Use the graph to solve the equation and inequalities. Write the solutions to the inequalities in interval notation. a.2x+8=12x+3b.2x+812x+3c.2x+812x+3 For Exercises 13-16, graph the equation. x2+y+522=9 For Exercises 13-16, graph the equation. fx=2x+3 For Exercises 13-16, graph the equation. gx=x+4+3 For Exercises 13-16, graph the equation. hx=x+3forx1x1forx1 17T For Exercises 18-19, determine if the function is even, odd, or neither. fx=x3x For Exercises 18-19, determine if the function is even, odd, or neither. gx=x4+x3+x 20T For Exercises 21-26, refer to the functions f,g,andh defined here. fx=x4gx=1x3hx=x5 Evaluatefh6.For Exercises 21-26, refer to the functions f,g,andh defined here. fx=x4gx=1x3hx=x5 Evaluategh5.For Exercises 21-26, refer to the functions f,g,andh defined here. fx=x4gx=1x3hx=x5 Evaluatehf1.For Exercises 21-26, refer to the functions f,g,andh defined here. fx=x4gx=1x3hx=x5 Find fgx and state the domain in interval notation.For Exercises 21-26, refer to the functions f,g,andh defined here. fx=x4gx=1x3hx=x5 Find and gfx state the domain in interval notation.26T Write two functions fandg such that hx=fgx. hx=x73 For fandg pictured, estimate the following. a.f+g3b.fg0c.gf3d.fg2e.Theintervalsoverwhichfisincreasing.f.Theintervalsoverwhichgisdecreasing.29T 30T 1CRE 2CRE 3CRE 4CRE 5CRE 6CRE 7CRE 8CRE 9CRE 10CRE Write an absolute value expression that represents the distance between the points xand7 on the line.12CRE 13CRE 14CRE 15CRE 16CRE 17CRE 18CRE 19CRE 20CRE Find the distance between the points 1,4and3,6 . Give the exact distance and an approximation to 2 decimal places.Determine if the points X6,4,Y2,2,andZ0,5 form the vertices of a right triangle.3SP 4SP 5SP Given the equation y=x24, a.Findthex-intercepts.b.Findy-intercepts.7SP In a rectangular coordinate system, the point where the x-andy-axes meet is called the .2PE 3PE 4PE 5PE 6PE A y-intercept of a graph has an x-coordinate of .8PE 9PE For Exercises 9-10, plot the points on a rectangular coordinate system. A2,5B92,73C3.6,2.1D5,E3.4,0F0,3 For Exercises 11-18, a. Find the exact distance between the points. (See Examples 1) b. Find the midpoint of the line segment whose endpoints are the given points. (See Example 3) 2,7and4,11 12PE For Exercises 11-18, a. Find the exact distance between the points. (See Examples 1) b. Find the midpoint of the line segment whose endpoints are the given points. (See Example 3) 7,4and2,5 For Exercises 11-18, a. Find the exact distance between the points. (See Examples 1) b. Find the midpoint of the line segment whose endpoints are the given points. (See Example 3) 3,6and4,1 15PE For Exercises 11-18, a. Find the exact distance between the points. (See Examples 1) b. Find the midpoint of the line segment whose endpoints are the given points. (See Example 3) 37.1,24.7and31.1,32.7 17PE 18PE 19PE For Exercises 19-22, determine if the given points form the vertices of a right triangle. (See Example 2) 1,2,3,0and3,2 21PE For Exercises 19-22, determine if the given points form the vertices of a right triangle. (See Example 2) 6,2,3,1,and1,2 For Exercises 23-24, determine if the given points are solutions to the equation. x2+y=1a.2,3b.4,17c.12,34 For Exercises 23-24, determine if the given points are solutions to the equation. x3y=4a.1,2b.2,3c.110,1110 25PE For Exercises 25-30, identify the set of value x for which y will be a real number. y=2x+7 For Exercises 25-30, identify the set of value x for which y will be a real number. y=x10 28PE For Exercises 25-30, identify the set of value x for which y will be a real number. y=1.5x 30PE For Exercises 31-44, graph the equation by plotting points. (See Examples 4-5) y=x For Exercises 31-44, graph the equation by plotting points. (See Examples 4-5) y=x2 33PE For Exercises 31-44, graph the equation by plotting points. (See Examples 4-5) y=x For Exercises 31-44, graph the equation by plotting points. (See Examples 4-5) y=x3 For Exercises 31-44, graph the equation by plotting points. (See Examples 4-5) y=1x For Exercises 31-44, graph the equation by plotting points. (See Examples 4-5) yx=2 38PE 39PE For Exercises 31-44, graph the equation by plotting points. (See Examples 4-5) y2x+1=0 For Exercises 31-44, graph the equation by plotting points. (See Examples 4-5) x=y+1 For Exercises 31-44, graph the equation by plotting points. (See Examples 4-5) x=y3 43PE 44PE 45PE For Exercises 45-50, estimate the x-andy-intercepts from the graph.For Exercises 45-50, estimate the x-andy-intercepts from the graph.48PE 49PE For Exercises 45-50, estimate the x-andy-intercepts from the graph.For Exercises 51-62, find the x-andy-intercepts. (See Example 6) 2x+4y=12 For Exercises 51-62, find the x-andy-intercepts. (See Example 6) 3x5y=60 For Exercises 51-62, find the x-andy-intercepts. (See Example 6) x2+y=9 For Exercises 51-62, find the x-andy-intercepts. (See Example 6) x2=y+16 55PE For Exercises 51-62, find the x-andy-intercepts. (See Example 6) y=x+43 For Exercises 51-62, find the x-andy-intercepts. (See Example 6) x=y21 For Exercises 51-62, find the x-andy-intercepts. (See Example 6) x=y24 For Exercises 51-62, find the x-andy-intercepts. (See Example 6) x=y For Exercises 51-62, find the x-andy-intercepts. (See Example 6) x=5y For Exercises 51-62, find the x-andy-intercepts. (See Example 6) x324+y429=1 62PE A map of a wilderness area is drawn with the origin placed at the parking area. Two fire observation platforms are located at points AandB . If a fire is located at point C, determine the distance to the fire from each observation platform.A map of a state park is draw so that the origin is placed at the visitor center. The distance between grip lines is 1 mi. Suppose that two hikers are located at points AandB . a. Determine the distance between the hikers. b. If the hikers want to meet for lunch, determine the located of the midpoint between the hikers.The position of an object in a video game is represented by an ordered pair. The coordinates of the ordered pair give the number of pixels ho horizontally and vertically from the origin. Use this scenario for Exercises 65-66. a. Suppose that player A is located at 36,315 and player B is located at 410,53. How far apart are the players? Round to the nearest pixel. b. If the two players move directly toward each other at the same speed, where will they meet? c. If player A moves three times faster than player B, where will they meet? Round to the neatest pixel.66PE Verify that the points A0,0,Bx,0,andC12x,32x make up the vertices of an equilateral triangle.Verify that the points A0,0,Bx,0,andC0,x make up the vertices of an isosceles right triangle (an isosceles triangle has two sides of equal length).69PE For Exercises 69-70, assume that the units shown in the grid are in feet. a. Determine the exact length and width of the rectangle shown. b. Determine the perimeter and area.71PE For Exercises 71-72, the endpoints of a diameter of a circle are shown. Find the center and radius of the circle.For Exercises 73-74, an isosceles triangle is shown. Find the area of the triangle. Assume that the units shown un the grid are in meters.74PE For Exercises 75-78, determine if points A,B,andC are collinear. Three points are collinear if they all fall on the same line. There are several ways that we can determine if three points, A,B,andC are collinear. One method is to determine if the sum of the lengths of the segments ABandBC equal the length of AC . 2,2,4,3,and8,5 For Exercises 75-78, determine if points A,B,andC are collinear. Three points are collinear if they all fall on the same line. There are several ways that we can determine if three points, A,B,andC are collinear. One method is to determine if the sum of the lengths of the segments ABandBC equal the length of AC . 2,1.5,4,2,and8,3 77PE For Exercises 75-78, determine if points A,B,andC are collinear. Three points are collinear if they all fall on the same line. There are several ways that we can determine if three points, A,B,andC are collinear. One method is to determine if the sum of the lengths of the segments ABandBC equal the length of AC . 1,5,0,3,and5,13 Suppose that d represents the distance between two points x1,y1andx2,y2. Explain how the distance formula is developed from the Pythagorean theorem.80PE Explain how to find the x-andy-intercepts from an equation in the variables xandy.82PE 83PE A point in three-dimensional space can be represented in a three-dimensional coordinate system. In such a case, a z-axis is taken perpendicular to both the x-andy-axes. A point P is assigned an ordered triple Px,y,z relative to a fixed origin where the three axes meet. For Exercises 83-86, determine the distance between the two given points in space. Use the distance formula d=x2x12+y2y12+z2z12 . 6,4,1and2,3,1 85PE A point in three-dimensional space can be represented in a three-dimensional coordinate system. In such a case, a z-axis is taken perpendicular to both the x-andy-axes. A point P is assigned an ordered triple Px,y,z relative to a fixed origin where the three axes meet. For Exercises 83-86, determine the distance between the two given points in space. Use the distance formula d=x2x12+y2y12+z2z12 . 9,5,3and2,0,1 What is meant by a viewing window on a graphing device?Which of the viewing windows would show both the x-andy-intercepts of the graph of 780x42y=5460? a.20,20,2by40,40,10b.10,10,1by10,10,1c.10,10,1by10,150,10d.10,10,1by150,10,10 For Exercises 89-92, graph the equation with a graphing utility on the given viewing window. (See Example 7) y=2x5on10,10,1by10,10,1 For Exercises 89-92, graph the equation with a graphing utility on the given viewing window. (See Example 7) y=4x+1on10,10,1by10,10,1 For Exercises 89-92, graph the equation with a graphing utility on the given viewing window. (See Example 7) y=1400x21200xon5,5,1by1000,2000,500 For Exercises 89-92, graph the equation with a graphing utility on the given viewing window. (See Example 7) y=800x2+600xon5,5,1by1000,500,200 For Exercises 93-94, graph the equations on the standard viewing window. (See Example 7) a.y=x3b.y=x9 For Exercises 93-94, graph the equations on the standard viewing window. (See Example 7) a.y=x+4b.y=x2 1SP 2SP 3SP Write the equation in the form xh2+yk2=r2 , and identify the solution set. x2+y2+2x+5=0 A is the set of all points in a equidistant from a fixed point called the .2PE 3PE 4PE 5PE 6PE 7PE 8PE 9PE 10PE 11PE 12PE 13PE 14PE 15PE 16PE 17PE 18PE 19PE 20PE 21PE 22PE 23PE 24PE 25PE 26PE 27PE 28PE 29PE 30PE 31PE 32PE Write an equation that represent the set of points that are 5 units from 8,11.Write an equation that represent the set of points that are 9 units from 4,16.35PE Write an equation of the circle that is tangent to both axes with radius 11 and center in Quadrant III.Determine the solution set for the equation x+12+y52=0.38PE 39PE Determine the solution set for the equation x+152+y32=25.For Exercise 41-54, write the equation in the form xh2+yk2=c. Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) x2+y2+6x2y+6=0 For Exercise 41-54, write the equation in the form xh2+yk2=c. Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) x2+y2+12x14y+84=0 For Exercise 41-54, write the equation in the form xh2+yk2=c. Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) x2+y222x+6y+129=0 For Exercise 41-54, write the equation in the form xh2+yk2=c. Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) x2+y210x+4y20=0 For Exercise 41-54, write the equation in the form xh2+yk2=c. Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) x2+y220y4=0 For Exercise 41-54, write the equation in the form xh2+yk2=c. Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) x2+y2+22x4=0 For Exercise 41-54, write the equation in the form xh2+yk2=c. Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) 10x2+10y280x+200y+920=0 48PE 49PE For Exercise 41-54, write the equation in the form xh2+yk2=c. Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) x2+y210x22y+155=0 For Exercise 41-54, write the equation in the form xh2+yk2=c. Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) 4x2+4y220y+25=0 For Exercise 41-54, write the equation in the form xh2+yk2=c. Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) 4x2+4y212x+9=0 53PE For Exercise 41-54, write the equation in the form xh2+yk2=c. Then if the equation represents a circle, identify the center and radius. If the equation represents a degenerate case, give the solution set. (See Examples 3-4) x2+y223x53y59=0 A cell tower is a site where antennas, transmitters, and receivers are placed to create a cellular network. Suppose that a cell tower is located at a point A(4, 6) on a map and its range is 1.5 mi. Write an equation that represents the boundary of the area that can receive a signal from the tower. Assume that all distances are in miles.A radar transmitter on a ship has a range of 20 nautical miles. If the ship is located at a point 32,40 on a map, write an equation for the boundary of the area within the range of the ship's radar. Assume that all distances on the map are represented in nautical miles.Suppose that three geological study areas are set up on a map at points A4,12,B11,3,andC0,1, where all units are in miles. Based on the speed of compression waves, scientists estimate the distances from the study areas to the epicenter of an earthquake to be 13 mi, 5 mi, and 10 mi. respectively. Graph three circles whose centers are located at the study areas and whose radii are the given distances to the earthquake. Then estimate the location of the earthquake.58PE State the definition of a circle.60PE Find all values of y such that the distance is 4,yand2,6 is 10 units.Find all values of x such that the distance between x,1and4,2 is 5 units.63PE Find all points on the line y=x that are 4 units from 4,6.The general form of an equation of a circle is xh2+yk2=r2. If we solve the equation for x we get equation of the form x=hr2yk2. The equation x=h+r2yk2 represents the graph of the corresponding right side semicircle, and the equation x=hr2yk2 represents the graph of the left-side semicircle likewise, if we solve for y, we have x=kr2yh2 . These equations represent the top and bottom semicircles. For Exercise 65-68, graph the equations. a.y=16x2b.y=16x2c.x=16y2d.x=16y2 The general form of an equation of a circle is xh2+yk2=r2. If we solve the equation for x we get equation of the form x=hr2yk2. The equation x=h+r2yk2 represents the graph of the corresponding right side semicircle, and the equation x=hr2yk2 represents the graph of the left-side semicircle likewise, if we solve for y, we have x=kr2yh2 . These equations represent the top and bottom semicircles. For Exercise 65-68, graph the equations. a.y=9x2b.y=9x2c.x=9y2d.x=9y2 The general form of an equation of a circle is xh2+yk2=r2. If we solve the equation for x we get equation of the form x=hr2yk2. The equation x=h+r2yk2 represents the graph of the corresponding right side semicircle, and the equation x=hr2yk2 represents the graph of the left-side semicircle likewise, if we solve for y, we have x=kr2yh2 . These equations represent the top and bottom semicircles. For Exercise 65-68, graph the equations. a.x=19y22b.x=1+9y22c.y=29x+12d.y=2+9x+12 The general form of an equation of a circle is xh2+yk2=r2. If we solve the equation for x we get equation of the form x=hr2yk2. The equation x=h+r2yk2 represents the graph of the corresponding right side semicircle, and the equation x=hr2yk2 represents the graph of the left-side semicircle likewise, if we solve for y, we have x=kr2yh2 . These equations represent the top and bottom semicircles. For Exercise 65-68, graph the equations. a.x=34y+22b.x=3+4y+22c.y=24x32d.y=2+4x32 Find the shortest distance from the origin to a point in the circle defined by x2+y26x12y+41=0.Find the shortest distance from the origin to a point in the circle defined by x2+y2+4x12y+31=0 .For Exercises 71-74, use a graphing calculator to graph the circles on an appropriate square viewing window. x2+y2=36 For Exercises 71-74, use a graphing calculator to graph the circles on an appropriate square viewing window. x2+y2=49 For Exercises 71-74, use a graphing calculator to graph the circles on an appropriate square viewing window. x182+y+202=80 For Exercises 71-74, use a graphing calculator to graph the circles on an appropriate square viewing window. x+0.042+y0.022=0.01 For the table shown, a. Write the set of ordered pairs that defines the relation. b. Write the domain. c. Write the range.Determine if the relation defines y as a function of x . a.8,4,3,1,5,4b.3,2,9,5,1,0,3,1 Determine if the given relation defines y as a function of x.Determine if the relation defines y as a function of x. b.y+1=xc.x2+y2=25 Evaluate the function defined by hx=4x3 for the given values of x. a.h3b.h1c.h0d.h1e.h3 Evaluate the function defined by fx=x2+4x for the given values of x. a.ftb.fa+h Find the x-andy-intercepts of the function defined by fx=x5.Determine the domain and range for the functions shown.Write the domain of each function in interval notation. a.fx=x23x+1b.gx=x25c.kx=x+3d.px=2x2+3x Use the function f pictured to find: a.f2.b.f4.c.Allxforwhichfx=3.d.Allxforwhichfx=1.e.Thex-intercepts.f.They-intercept.g.Thedomainoff.h.Therangeoff.A set of ordered pairs x,y is called a in xandy . The set of x values in the relation is called the of the relation. The set of values is called the range of the relation.Given a function defined by y=fx, the statement f2=4 is equivalent to what ordered pair?Given a function defined by y=fx, to find the -intercept, evaluate f0 .Given a function defined by y=fx, to find the x-intercepts, substitute 0 for and solve x .Given fx=x+1x+5 , the domain is restricted so that x.Given gx=x5, the domain is restricted so that x.Consider a relation that defines the height y of a tree for a given time t after it is planted. Does this relation define y as a function of t ? Explain.Consider a relation that define a time y during the course of a year when the temperature T in Fort Collins, Colorado, is 70 . Does this relation define y as a function of T ? Explain.For Exercises 9-12, a. Write a set of ordered pairs x,y that defines the relation. b. Write the domain of the relation. c. Write the range of the relation. d. Determine if the relation defines y as a function of x . (See Examples 1-2)For Exercises 9-12, a. Write a set of ordered pairs x,y that defines the relation. b. Write the domain of the relation. c. Write the range of the relation. d. Determine if the relation defines y as a function of x . (See Examples 1-2)For Exercises 9-12, a. Write a set of ordered pairs x,y that defines the relation. b. Write the domain of the relation. c. Write the range of the relation. d. Determine if the relation defines y as a function of x . (See Examples 1-2)For Exercises 9-12, a. Write a set of ordered pairs x,y that defines the relation. b. Write the domain of the relation. c. Write the range of the relation. d. Determine if the relation defines y as a function of x . (See Examples 1-2)Answer true or false. All relations are relations.Answer true or false. All relations are functions.For Exercises 15-32, determine if the relation defines y as a function of x . (See Example 3-4)For Exercises 15-32, determine if the relation defines y as a function of x . (See Example 3-4)For Exercises 15-32, determine if the relation defines y as a function of x . (See Example 3-4)For Exercises 15-32, determine if the relation defines y as a function of x . (See Example 3-4)19PE For Exercises 15-32, determine if the relation defines y as a function of x . (See Example 3-4)For Exercises 15-32, determine if the relation defines y as a function of x . (See Example 3-4)For Exercises 15-32, determine if the relation defines y as a function of x . (See Example 3-4)For Exercises 15-32, determine if the relation defines y as a function of x . (See Example 3-4)24PE For Exercises 15-32, determine if the relation defines y as a function of x . (See Example 3-4)For Exercises 15-32, determine if the relation defines y as a function of x . (See Example 3-4)27PE For Exercises 15-32, determine if the relation defines y as a function of x . (See Example 3-4) x+32+y+42=1 29PE 30PE For Exercises 15-32, determine if the relation defines y as a function of x . (See Example 3-4) a.y=x2b.x=y2 For Exercises 15-32, determine if the relation defines y as a function of x . (See Example 3-4) a.y=xb.x=y 33PE The statement g7=5 corresponds to what ordered pair?For Exercises 35-56, evaluate the function for the given of x . (See Example 5-6) fx=x2+3xgx=1xhx=5kx=x+1 a.f2b.f1c.f0d.f1e.f2 36PE 37PE For Exercises 35-56, evaluate the function for the given of x . (See Example 5-6) fx=x2+3xgx=1xhx=5kx=x+1 a.k2b.k1c.k0d.k1e.k3 For Exercises 35-56, evaluate the function for the given of x . (See Example 5-6) fx=x2+3xgx=1xhx=5kx=x+1 g3 40PE 41PE For Exercises 35-56, evaluate the function for the given of x . (See Example 5-6) fx=x2+3xgx=1xhx=5kx=x+1 h7 For Exercises 35-56, evaluate the function for the given of x . (See Example 5-6) fx=x2+3xgx=1xhx=5kx=x+1 k5 44PE 45PE For Exercises 35-56, evaluate the function for the given of x . (See Example 5-6) fx=x2+3xgx=1xhx=5kx=x+1 f5 47PE For Exercises 35-56, evaluate the function for the given of x . (See Example 5-6) fx=x2+3xgx=1xhx=5kx=x+1 fa For Exercises 35-56, evaluate the function for the given of x . (See Example 5-6) fx=x2+3xgx=1xhx=5kx=x+1 kx+h 50PE 51PE For Exercises 35-56, evaluate the function for the given of x . (See Example 5-6) fx=x2+3xgx=1xhx=5kx=x+1 ft3 53PE 54PE For Exercises 35-56, evaluate the function for the given of x . (See Example 5-6) fx=x2+3xgx=1xhx=5kx=x+1 fx+h For Exercises 35-56, evaluate the function for the given of x . (See Example 5-6) fx=x2+3xgx=1xhx=5kx=x+1 gx+h 57PE For Exercises 57-62, find and simplify fx+h. (See Example 6) fx=2x2+6x3 59PE

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