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All Textbook Solutions for Precalculus

For Exercises 19-26, refer to the functions r,p,andq. Find the indicated function and write the domain in interval notation. (See Example 3) rx=3xpx=x2+3xqx=1x qrx For Exercises 19-26, refer to the functions r,p,andq. Find the indicated function and write the domain in interval notation. (See Example 3) rx=3xpx=x2+3xqx=1x pqx For Exercises 19-26, refer to the functions r,p,andq. Find the indicated function and write the domain in interval notation. (See Example 3) rx=3xpx=x2+3xqx=1x rqx For Exercises 27-32, refer to functions s,t,andv. Find the indicated function and write the domain in interval notation. (See Example 3) sx=x2x29tx=x32xvx=x+3 stx For Exercises 27-32, refer to functions s,t,andv. Find the indicated function and write the domain in interval notation. (See Example 3) sx=x2x29tx=x32xvx=x+3 stx For Exercises 27-32, refer to functions s,t,andv. Find the indicated function and write the domain in interval notation. (See Example 3) sx=x2x29tx=x32xvx=x+3 s+tx For Exercises 27-32, refer to functions s,t,andv. Find the indicated function and write the domain in interval notation. (See Example 3) sx=x2x29tx=x32xvx=x+3 stx For Exercises 27-32, refer to functions s,t,andv. Find the indicated function and write the domain in interval notation. (See Example 3) sx=x2x29tx=x32xvx=x+3 svx For Exercises 27-32, refer to functions s,t,andv. Find the indicated function and write the domain in interval notation. (See Example 3) sx=x2x29tx=x32xvx=x+3 vsx For Exercises 33-36, a function is given. (See Example 4-5) a.Findfx+h.b.Findfx+hfxh. fx=5x+9 For Exercises 33-36, a function is given. (See Example 4-5) a.Findfx+h.b.Findfx+hfxh. fx=8x+4 For Exercises 33-36, a function is given. (See Example 4-5) a.Findfx+h.b.Findfx+hfxh. fx=x2+4x For Exercises 33-36, a function is given. (See Example 4-5) a.Findfx+h.b.Findfx+hfxh. fx=x23x For Exercises 37-44, find the difference quotient and simplify. (See Example 4-5) fx=2x+5 For Exercises 37-44, find the difference quotient and simplify. (See Example 4-5) fx=3x+8 For Exercises 37-44, find the difference quotient and simplify. (See Example 4-5) fx=5x24x+2 For Exercises 37-44, find the difference quotient and simplify. (See Example 4-5) fx=4x22x+6 For Exercises 37-44, find the difference quotient and simplify. (See Example 4-5) fx=x3+5 For Exercises 37-44, find the difference quotient and simplify. (See Example 4-5) fx=x32 For Exercises 37-44, find the difference quotient and simplify. (See Example 4-5) fx=1x For Exercises 37-44, find the difference quotient and simplify. (See Example 4-5) fx=1x+2 Given fx=4x, a. Find the difference quotient (do not simplify). b. Evaluate the difference quotient for x=1, and the following values of h:h=1,h=0.1,h=0.01,andh=0.001. Round to 4 decimal places. c. What value does the difference quotient seem to be approaching as h gets close to 0?Given fx=12x, a. Find the difference quotient (do not simplify). b. Evaluate the difference quotient for x=2, and the following values of h:h=0.1,h=0.01,h=0.001andh=0.0001. Round to 4 decimal places. c. What value does the difference quotient seem to be approaching as h gets close to 0?For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 fg8 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 hg2 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 hf1 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 gf3 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 fg18 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 fh1 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 gf5 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 hf2 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 hf3 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 hg72 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 gf1 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 gf4 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 ff3 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 hh4 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 fhg2 For Exercises 47-62, refer to functions f,g,andh. Evaluate the functions for the given values of x. (See Example 6) fx=x34xgx=2xhx=2x+3 fhg8 Given fx=2x+4andgx=x2, a.Findfgx.b.Findgfx.c.Istheoperationoffunctionco,positioncommulative?Given kx=3x+1andmx=1x, a.Findkmx.b.Findmkx.c.Iskmx=mkx?For Exercises 65-76, refer to function to functions m,n,p,q,andr. Find the indicated function and write the domain in interval notation. (See Examples 7-9) mx=x+8nx=x5px=x29xqx=1x10rx=2x+3 npx For Exercises 65-76, refer to function to functions m,n,p,q,andr. Find the indicated function and write the domain in interval notation. (See Examples 7-9) mx=x+8nx=x5px=x29xqx=1x10rx=2x+3 pnx For Exercises 65-76, refer to function to functions m,n,p,q,andr. Find the indicated function and write the domain in interval notation. (See Examples 7-9) mx=x+8nx=x5px=x29xqx=1x10rx=2x+3 mnx For Exercises 65-76, refer to function to functions m,n,p,q,andr. Find the indicated function and write the domain in interval notation. (See Examples 7-9) mx=x+8nx=x5px=x29xqx=1x10rx=2x+3 nmx For Exercises 65-76, refer to function to functions m,n,p,q,andr. Find the indicated function and write the domain in interval notation. (See Examples 7-9) mx=x+8nx=x5px=x29xqx=1x10rx=2x+3 qnx For Exercises 65-76, refer to function to functions m,n,p,q,andr. Find the indicated function and write the domain in interval notation. (See Examples 7-9) mx=x+8nx=x5px=x29xqx=1x10rx=2x+3 qpx For Exercises 65-76, refer to function to functions m,n,p,q,andr. Find the indicated function and write the domain in interval notation. (See Examples 7-9) mx=x+8nx=x5px=x29xqx=1x10rx=2x+3 qrx For Exercises 65-76, refer to function to functions m,n,p,q,andr. Find the indicated function and write the domain in interval notation. (See Examples 7-9) mx=x+8nx=x5px=x29xqx=1x10rx=2x+3 qmx For Exercises 65-76, refer to function to functions m,n,p,q,andr. Find the indicated function and write the domain in interval notation. (See Examples 7-9) mx=x+8nx=x5px=x29xqx=1x10rx=2x+3 nrx 74PE For Exercises 65-76, refer to function to functions m,n,p,q,andr. Find the indicated function and write the domain in interval notation. (See Examples 7-9) mx=x+8nx=x5px=x29xqx=1x10rx=2x+3 qqx For Exercises 65-76, refer to function to functions m,n,p,q,andr. Find the indicated function and write the domain in interval notation. (See Examples 7-9) mx=x+8nx=x5px=x29xqx=1x10rx=2x+3 ppx For Exercises 77-80, find fgx and write the domain in interval notation. (See Example 9) fx=3x216,gx=2x For Exercises 77-80, find fgx and write the domain in interval notation. (See Example 9) fx=4x29,gx=3x For Exercises 77-80, find fgx and write the domain in interval notation. (See Example 9) fx=xx1,gx=9x216 For Exercises 77-80, find fgx and write the domain in interval notation. (See Example 9) fx=xx+4,gx=3x21 Given fx=1x2,findffx and write the domain in interval notation.Given gx=x3,findggx and write the domain in interval notation.83PE 84PE For Exercises 83-86, find the indicated functions. fx=2x+1gx=x2hx=x3 hgfx 86PE A law office orders business stationery. The cost is $21.95 per box. (See Example 10) a. Write a function that represents the cost Cxin$ for x boxes of stationery. b. There is a 6 sales tax on the cost of merchandise and $10.99 for shipping. Write a function that represents the total cost Ta for a dollars spent in merchandise and shipping. c. Find TCx. d. Find TC4 and interpret its meaning in the context of this problem.The cost to buy tickets online for a dance show is $60 per ticket. a. Write a function that represents the cost Cxin$ for x tickets to the show. b. There is a sales tax of 5.5 and a processing fee of $8.00 for a group of tickets. Write a function that represents the total cost Ta for a dollars spent on tickets. c. Find TCx. d. Find TC6 and interpret its meaning in the context of this problem A bicycle wheel turns at a rate of 80 revolutions per minute (rpm). a. Write a function that represents the number of revolutions rt in t minutes. b. For each revolution of the wheels, the bicycle travels 7.2 ft. Write a function that represents the distance traveled drinft for r revolutions of the wheel. c. Find drt and interpret the meaning in the context of this problem. d. Evaluate dr30. and interpret the meaning in the context of this problem.While on vacation in France, Sadie bought a box of almond croissants. Each croissant cost 2.40 (euros). a. Write a function that represents the cost Cx (in euros) for x croissants. b. At the time of the purchase, the exchange rate was $1=0.80. Write a function that represents the amount DCin$ for C euros spent c. Find DCx and interpret the meaning in the context of this problem. d. Evaluate DC12 and interpret the meaning in the context of this problem.For Exercises 91-98, find two functions fandg such that hx=fgx. (See Example 11) hx=x+72 92PE For Exercises 91-98, find two functions fandg such that hx=fgx. (See Example 11) hx=2x+13 94PE For Exercises 91-98, find two functions fandg such that hx=fgx. (See Example 11) hx=2x23 96PE For Exercises 91-98, find two functions fandg such that hx=fgx. (See Example 11) hx=5x+4 98PE 99PE For Exercises 99-102, the graphs of two functions are shown. Evaluate the function at given value of x, if possible. (See Example 12) a.f+g0b.gf1c.gf2d.fg3e.fg3f.gf0g.gf4 101PE 102PE For Exercises 103-110, refer to the functions fandg and evaluate the functions for the given values of x. f=2,4,6,1,4,2,0,3,1,6andg=4,3,0,6,5,7,6,0 f+g4 For Exercises 103-110, refer to the functions fandg and evaluate the functions for the given values of x. f=2,4,6,1,4,2,0,3,1,6andg=4,3,0,6,5,7,6,0 gf0 For Exercises 103-110, refer to the functions fandg and evaluate the functions for the given values of x. f=2,4,6,1,4,2,0,3,1,6andg=4,3,0,6,5,7,6,0 gf2 For Exercises 103-110, refer to the functions fandg and evaluate the functions for the given values of x. f=2,4,6,1,4,2,0,3,1,6andg=4,3,0,6,5,7,6,0 fg0 107PE For Exercises 103-110, refer to the functions fandg and evaluate the functions for the given values of x. f=2,4,6,1,4,2,0,3,1,6andg=4,3,0,6,5,7,6,0 ff1 109PE 110PE 111PE Consider a right circular cone with given height h. The volume of the cone as a function of its radius r is given by vr=13r2h. Consider a right circular cone with fixed height h=6 in. a Write the diameter d of the cone as a function of the radius r. b. Write the radius r as a function of the diameter d. c. Find Vrd and interpret its meaning. Assume that h=6 in.113PE 114PE Suppose that a function H gives the high temperature HxinoF for day x. Suppose that a function L gives the low temperature LxinoF for day x. What does H+L2x represent?116PE 117PE Given functions fandg, explain how to determine the domain of fgx.119PE Explain what the difference quotient represents.121PE 122PE A car traveling 60 mph (88 ft/sec) undergoes a constant deceleration until it comes to rest approximately 9.09 sec later. The distance dt (in ft) that the car travels t seconds after the brakes are applied is given by dt=4.84t2+88t,where0t9.09. (See Example 5) a. Find the difference quotient dt+hdth. Use the difference quotient to determine the average rate of speed on the following intervals for t. b.0,2c.2,4d.4,6e.6,8 A car accelerates from 0 to 60 mph (88 ft/sec) in 8.8 sec. The distance dt (in ft) that the car travels t seconds after motion begins is given by dt=5t2, where 0,t8.8. a. Find the difference quotient dt+hdth. Use the difference quotient to determine the average rate of speed on the following intervals for t. b.0,2c.2,4d.4,6e.6,8 If a is b plus eight, and c is the square of a, write c as a function of b.If q is r minus seven, and s is the square of q, write s as a function of r.If x is twice y, and z is four less than x, write z as a function of y.If m is one-third of n, and p is two less than m, write p as a function of n.Given fx=4x2+13, define functions m,n,h,andk such that fx=mnhkx .Given fx=2x34, define functions m,n,h,andk such that fx=mnhkx .Given fx=x+52+2, identity the vertex of the graph of the parabola.For Exercises 2-3, a. Write the equation in vertex form: fx=axh2+k. b. Determine whether the parabola opens upward or downward. c. Identify the vertex. d. Identify the x-intercepts. e. Identify the y-intercepts. f. Sketch the function. g. Determine the axis of symmetry. h. Determine the minimum or maximum value of the function. i. State the domain and range. fx=x28x+15 For Exercises 2-3, a. Write the equation in vertex form: fx=axh2+k. b. Determine whether the parabola opens upward or downward. c. Identify the vertex. d. Identify the x-intercepts. e. Identify the y-intercepts. f. Sketch the function. g. Determine the axis of symmetry. h. Determine the minimum or maximum value of the function. i. State the domain and range. fx=2x2+4x+6 a. Use the vertex formula to determine the vertex of fx=2x2+12x+19. b. Based on the location of the vertex and the orientation of the parabola, how many x-intercepts will the graph of fx=2x2+12x+19 have?Suppose that a farmer encloses a corral for cattle adjacent to a river. No fencing is used by the river. a. If he has 180 yd of fencing, what dimensions should he use to maximize the area? b. What is the maximum area?Suppose that p is the probability that a randomly selected person is left-handed. The value 1p is the probability that the person is not left-handed. in a sample of 100 people, the function Vp=100p1p represents the variance of the number of left-handed people in a group of 100. a. What value of p maximizes the variance? b. What is the maximum variance?The annual expenditure for cell phones and cellular service varies in part by the age of an individual. The average annual expenditure Eain$ for individuals of age a (in yr) is given in the table. a. Use regression to find a quadratic function to model the data. b. At what age is the yearly expenditure for cell phones and cellular service the greatest? Round to the nearest year. c. What is the maximum yearly expenditure? Round to the nearest dollar.For Exercises 8-11, a. Determine the end behaviour of the graph of the function. b. Find all the zeros of the function and state their multiplicities. c. Determine the x-intercepts. d. Determine the y-intercepts. e. Is the function even, odd, or neither? f. Graph the function. fx=4x3+16x2+25x100 For Exercises 8-11, a. Determine the end behaviour of the graph of the function. b. Find all the zeros of the function and state their multiplicities. c. Determine the x-intercepts. d. Determine the y-intercepts. e. Is the function even, odd, or neither? f. Graph the function. fx=x410x2+9 For Exercises 8-11, a. Determine the end behaviour of the graph of the function. b. Find all the zeros of the function and state their multiplicities. c. Determine the x-intercepts. d. Determine the y-intercepts. e. Is the function even, odd, or neither? f. Graph the function. fx=x4+3x33x211x6 11RE Determine whether the intermediate value theorem guarantees that the function has on zero on the given interval. fx=2x35x26x+2a.2,1b.1,0c.0,1d.1,2 For Exercises 13-16, determine if the statement is true or false. If a statement is false, explain why. A fourth-degree polynomial has exactly three turning points.For Exercises 13-16, determine if the statement is true or false. If a statement is false, explain why. A fourth-degree polynomial has at most three turning points.For Exercises 13-16, determine if the statement is true or false. If a statement is false, explain why. There is exactly one polynomial with zeros of 2, 3, and 4.For Exercises 13-16, determine if the statement is true or false. If a statement is false, explain why. If c is a real zero of an odd polynomial function, then c is also a zero.For Exercises 17-18, a. Divide the polynomials. b. Identify the dividend, division, quotient, and remainder. 2x4+x3+4x1x2+x3 For Exercises 17-18, a. Divide the polynomials. b. Identify the dividend, division, quotient, and remainder. 3x42x315x2+22x83x2 For Exercises 19-20, use synthetic division to divide the polynomials. 2x5+x25x+1x+2 For Exercises 19-20, use synthetic division to divide the polynomials. x4+3x3x2+7x+2x3 21RE For Exercises 21-22, use the remainder theorem to evaluate the polynomial for the given values of x. fx=x4+2x34x210x5;f5 For Exercises 23-24, use the remainder theorem to determine if the given number c is a zero of the polynomial. fx=3x4+13x3+2x2+52x40a.c=2b.c=23 For Exercises 23-24, use the remainder theorem to determine if the given number c is a zero of the polynomial. fx=x4+6x3+9x2+24x+20a.c=5b.c=2i For Exercises 25-26, use the factor theorem to determine if the given binomial is a factor of the polynomial. fx=x3+4x2+9x+36a.x+4b.x3i For Exercises 25-26, use the factor theorem to determine if the given binomial is a factor of the polynomial. fx=x24x46a.x+2b.x252 Factor fx=15x367x2+26x+8, given that 23 is a zero of fx.Write a third-degree polynomial fx with zeros 1,32,and32.Write a third-degree polynomial fx with integer coefficients and zeros of 14,12, and 3.Given fx=2x57x4+9x318x2+4x+40, a. How many zeros does fx have (including multiplicities)? b. List the possible rational zeros of fx . c. Find all rational zeros of fx . d. Find all the zeros of fx .Given fx=x4+4x3+2x28x8, a. How many zeros does fx have (including multiplicities)? b. List the possible rational zeros of fx . c. Find all rational zeros of fx . d. Find all the zeros of fx .32RE Given fx=x422x3+119x2+66x366 and that 11i is a zero of fx . a. Find all the zeros of fx . b. Factor fx as a product of linear factors. c. Solve the equation fx=0.Write a polynomial fx of lowest degree with real coefficients and with zeros 23i (multiplicity 1) and 0 (multiplicity 2).Write a third-degree polynomial fx with integer coefficients and with zeros of 2iand53.For Exercises 36-37, determine the number of possible positive and negative real zeros for the given function. gx=3x7+4x62x2+5x4 For Exercises 36-37, determine the number of possible positive and negative real zeros for the given function. nx=x6+13x4+27x3+4x2+3 For Exercises 38-39. a. Determine if the upper bound theorem identifies the given number as an upper bound for the real zeros of fx. b. Determine if the lower bound theorem identifies the given number as a lower bound for the real zeros of fx. fx=x43x3+2x3a.2b.2 For Exercises 38-39. a. Determine if the upper bound theorem identifies the given number as an upper bound for the real zeros of fx. b. Determine if the lower bound theorem identifies the given number as a lower bound for the real zeros of fx. fx=x34x2+2x+1a.5b.2 Refer to the graph of y=fx and complete the statements. a.Asxfx.b.Asx2,fx.c.Asx2+,fx.d.Asx,fx. e. The graph is increasing over the interval(s) . f. The graph is decreasing over the interval(s) . g. The domain is . h. The range is . i. The vertical asymptote is the line . j. The horizontal asymptote is the line .For Exercises 41-42, determine the vertical asymptotes of the graph of the function. fx=x+42x2+x15 For Exercises 41-42, determine the vertical asymptotes of the graph of the function. gx=5x2+3 43RE For Exercises 43-45, a. Determine the horizontal asymptotes (if any). b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the horizontal asymptote. qx=2x23x+4x2+1 45RE 46RE 47RE 48RE For Exercises 48-51, graph the function. kx=x2x2x12 For Exercises 48-51, graph the function. mx=x2+6x+9x For Exercises 48-51, graph the function. qx=12x2+6 After taking a certain class, the percentage of material retained Pt decreases with the number of months t after taking the class. Pt can be approximated by Pt=t+900.16t+1 a. Determine the percentage retained after 1 month, 4 months, and 6 months. Round to the nearest percent. b. As t becomes infinitely large, what percentage of material will be retained?53RE The graph of y=fx is given. Solve the inequalities. fx0fx0fx0fx0 55RE 56RE For Exercises 57-66, solve the inequalities. tt318 For Exercises 57-66, solve the inequalities. w3+w29w90 59RE For Exercises 57-66, solve the inequalities. 6x43x42x+230 For Exercises 57-66, solve the inequalities. z33z210z24 62RE For Exercises 57-66, solve the inequalities. 62xx20 64RE For Exercises 57-66, solve the inequalities. 3x22x 66RE A sports trainer has monthly costs of $80 for phone service and $40 for his website and advertising. In addition he pays a $15 fee to the gym for each session in which he works with a client. a. Write a function representing the average cost Cxin$ for x training sessions. b. Find the number of sessions the trainer needs if he wants the average cost to drop below $16 per session.A Child throws a ball straight upwards to his friend who is sitting in a tree 18 ft above ground level. a. If the ball leaves the child s hand at a height of 2 ft with an initial speed of 40 ft/sec, write a function representing the vertical position of the ball stinft in terms of the time t after the ball leaves the childâ€™s hand. b. Determine the tine interval for which the ball will be more than 18 ft high.For Exercises 69-71, write a variation model using k as the constant of variation. The mass m of an animal varies directly as the weight w of the animalâ€™s heart.For Exercises 69-71, write a variation model using k as the constant of variation. The value of x varies inversely to the square of p.For Exercises 69-71, write a variation model using k as the constant of variation. The variable y is jointly proportional to x and the square root of z, and inversely proportional to the cube of t.72RE 73RE The weight of a ball varies directly as the cube of its radius. A weighted exercise ball of radius 3 in. weighs 3.24. lb. How much would a ball weigh if its radius were 5 in?75RE The power in an electric circuit varies jointly as the current and the square of the resistance. If the power is l44 watts (W) when the current is 4 A and the resistance is 6 , find the power when the current is 3 A and the resistance is 10. .Coulomb's law states that the force F of attraction between two oppositely charged particles varies jointly as the magnitude of their electrical charges q1andq2 and inversely as the square of the distance d between the Particles. Find the effect on F of doubling q1andq2 and halving the distance between them.Given fx=2x212x+16, a. Write the equation in vertex form: fx=axh2+k. b. Determine whether the parabola opens upward or downward. c. Identify the vertex. d. Identify the x-intercepts. e. Identify the y-intercepts. f. Sketch the function. g. Determine the axis of symmetry. h. Determine the minimum or maximum value of the function. i. State the domain and range.2T 3T 4T Determine whether the intermediate value theorem guarantees that the function has a zero on the given interval. fx=x35x2+2x+5a.2,1b.1,0c.0,1d.1,2 a. Divide the polynomials. 2x44x3+x5x23x+1 b. Identify the dividend, divisor, quotient, and remainder.Given fx=5x4+47x3+80x251x9, a.Is35azerooffx?b.Is1azerosoffx?c.Isx+1afactoroffx?d.Isx+3afactoroffx?e.Usetheremaindertheoremtoevaluatef2.8T Given fx=3x4+7x312x214x+12, a. How many zeros does fx have (including multiplicities)? b. List the possible rational zeros. c. Determine if the upper bound theorem identifies 2 as an upper bound for the real zeros of fx . d. Determine if the lower bound theorem identifies 4 as a lower bound for the real zeros of fx . e. Revise the list of possible rational zeros based on the answer to parts (c)and (d). f. Find the rational zeros. g. Find all the zeros. h. Graph the function.Write a third-degree polynomial fx with integer coefficients and zeros of 15,23,and4.Determine the number of possible positive and negative real zeros for fx=6x74x5+2x43x2+1.For Exercises 12-14, determine the asymptotes (vertical, horizontal, and slant). rx=2x23x+5x7 For Exercises 12-14, determine the asymptotes (vertical, horizontal, and slant). px=3x+14x21 For Exercises 12-14, determine the asymptotes (vertical, horizontal, and slant). nx=5x22x+13x2+4 For Exercise 15-17, graph the function. mx=1x2+3 For Exercise 15-17, graph the function. hx=4x24 For Exercise 15-17, graph the function. kx=x22x+1x For Exercises 18-24, solve the inequality. c2c+20 For Exercises 18-24, solve the inequality. y313y12 For Exercises 18-24, solve the inequality. 2xx42x+130 21T 22T For Exercises 18-24, solve the inequality. 4x290 24T write a variation model using k as the constant of variation: Energy E varies directly as the square of the velocity v of the wind.26T The surface area of a cube varies directly as the square of the length of an edge. The surface area is 24ft2 when the length of an edge is 2 ft. Find the surface area of a cube with an edge that is 7 ft.28T The pressure of wind on a wall varies jointly as the area of the wall and the square of the velocity of the wed. If the velocity of the wind is tripled, what is the effect on the pressure on the wall?The population Pt of rabbits in a wildlife area t years after being introduced to the area is given by Pt=2000tt+1 a. Determine the number of rabbits after 1 yr, 5 yr, and 10 yr. Round to the nearest whole unit. b. What will the rabbit population approach as t approaches infinity?31T Suppose that a rocket is shot straight upward from ground level with an initial speed of 98 m/sec. a. Write a model that represents the height of the rocket st (in meters) t seconds after launch. b. When will the rocket reach its maximum height? c. What is the maximum height? d. Determine the time interval for which the rocket will be more than 200 m high. Round to the nearest tenth of a second.The number of yearly visits to physiciansâ€™ offices varies in part by the age of the patient. For the data shown in the table. a represents the age of patients (in yr) and na represents the corresponding number of visits to physiciansâ€™ offices per year. a. Use regression to find a quadratic function to model the data. b. At what age is the number of yearly visits to physiciansâ€™ offices the least? Round to the nearest year of age. c. What is the minimum number of yearly visits? Round to 1 decimal place.Repeat Example 1 with gx=x+221.2SP Repeat Example 3 with fx=x24x7.A quarterback throws a football with an initial velocity of 72 ft/sec at an angle of 25. The height of the ball can be modeled by ht=16t2+30.4t+5 , where ht is the height (in ft) and t is the time in seconds after release. a. Determine the time at which the ball will be at its maximum height. b. Determine the maximum height of the ball. c. Determine the amount of time required for the bail to reach the receiver's hands if the receiver catches the ball at a point 3 ft off the ground.5SP The funding ftin$millions for a drug rehabilitation center is given in the table for selected years t . a. Use regression to find a quadratic function to model the data. b. During what year is the funding the least? Round to the nearest year. c. What is the minimum yearly amount of funding received? Round to the nearest million.A function defined by fx=ax2+bx+ca0 is called a function.The vertical line drawn through the vertex of a quadratic function is called the of symmetry.Given fx=axh2+ka0, the vertex of the parabola is the point .Given fx=axh2+k,ifa0, the parabola opens (upward/downward) and the (minimum/maximum) value is .Given fx=axh2+k,ifa0, the parabola opens (upward/downward) and the (minimum/maximum) value is .The graph of fx=axh2+k,a0, is a parabola and the axis of symmetry is the line given by ____________ .For Exercises 7-14, a. Determine whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 1) fx=x42+1 For Exercises 7-14, a. Determine whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 1) gx=x+22+4 For Exercises 7-14, a. Determine whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 1) hx=2x+128 10PE For Exercises 7-14, a. Determine whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 1) mx=3x12 For Exercises 7-14, a. Determine whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 1) nx=12x+22 For Exercises 7-14, a. Determine whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 1) px=15x+42+1 14PE For Exercises 15-24, a. Write the function in vertex form. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 2) fx=x2+6x+5 For Exercises 15-24, a. Write the function in vertex form. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 2) gx=x2+8x+7 For Exercises 15-24, a. Write the function in vertex form. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 2) px=3x212x7 For Exercises 15-24, a. Write the function in vertex form. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 2) qx=2x24x3 For Exercises 15-24, a. Write the function in vertex form. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 2) cx=2x210x+4 For Exercises 15-24, a. Write the function in vertex form. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 2) dx=3x29x+8 For Exercises 15-24, a. Write the function in vertex form. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 2) hx=2x2+7x For Exercises 15-24, a. Write the function in vertex form. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 2) kx=3x28x For Exercises 15-24, a. Write the function in vertex form. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 2) px=x2+9x+17 For Exercises 15-24, a. Write the function in vertex form. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the function. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 2) qx=x2+11x+26 For Exercises 25-32, find the vertex of the parabola by applying the vertex formula. fx=3x242x91 For Exercises 25-32, find the vertex of the parabola by applying the vertex formula. gx=4x264x+107 For Exercises 25-32, find the vertex of the parabola by applying the vertex formula. ka=13a2+6a+1 For Exercises 25-32, find the vertex of the parabola by applying the vertex formula. jt=14t2+10t5 For Exercises 25-32, find the vertex of the parabola by applying the vertex formula. fc=4c25 For Exercises 25-32, find the vertex of the parabola by applying the vertex formula. ha=2a2+14 For Exercises 25-32, find the vertex of the parabola by applying the vertex formula. Px=1.2x21.8x3.6 (write the coordinates of the vertex as decimals.)For Exercises 25-32, find the vertex of the parabola by applying the vertex formula. Qx=7.5x22.25x+4.75 (write the coordinates of the vertex as decimals.)For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) gx=x2+2x4 For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) hx=x26x10 For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) fx=5x215x+3 For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) kx=2x210x5 For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) fx=2x2+3 For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) gx=x21 For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) fx=2x220x50 For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) mx=2x28x+8 For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) nx=x2x+3 For Exercises 33-42, a. State whether the graph of the parabola opens upward or downward. b. Identify the vertex. c. Determine the x-intercept(s). d. Determine the y-intercept. e. Sketch the graph. f. Determine the axis of symmetry. g. Determine the minimum or maximum value of the function. h. Write the domain and range in interval notation. (See Example 3) rx=x25x+7 The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt, If the price is too high, sales will drop. If the price is too low, the revenue brought in may not cover the cost to produce the shirts. After months of data collection, the sales team determines that the monthly profit is approximated by fp=50p2+1700p12,000, where p is the price per shirt and fp is the monthly profit based on that price. (See Example 4) a. Find the price that generates the maximum profit. b. Find the maximum profit. c. Find the price(s) that would enable the company to break even.The monthly profit fora company that makes decorative picture frames depends on the price per frame. The company determines that the profit is approximated by fp=80p2+3440p36,000, where p is the price per frame and fp is the monthly profit based on that price. a. Find the price that generates the maximum profit. b. Find the maximum profit. c. Find the price(s) that would enable the company to break even.A long jumper leaves the ground at an angle of 20o above the horizontal at a speed of11 m/sec. The height of the jumper can be modeled by hx=0.046x2+0.364x, where h is the jumperâ€™s height in meters and x is the horizontal distance from the point of launch. a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places. b. What is the maximum height of the long jumper? Round to 2 decimal places. c. What is the length of the jump? Round to 1 decimal place.A firefighter holds a hose 3 m off the ground and directs a stream of water toward a burning building. The water leaves the hose at an initial speed of 16 m/sec at an angle of 30o . The height of the water can be approximated by hx=0.026x2+0.577x+3, where hx is the height of the water in meters at a point x meters horizontally from the firefighter to the building. a. Determine the horizontal distance from the firefighter at which the maximum height of the water occurs. Round to 1 decimal place. b. What is the maximum height of the water? Round to 1 decimal place. c. The flow of water hits the house on the downward branch of the parabola at a height of 6 m. Now far is the firefighter front the house? Round to the nearest meter.The population pt of a culture of the bacterium Pseudomonas aeruginosa is given by Pt=1718t2+82,000t+10,000, where t is the time in hours since the culture was started. a. Determine the tine at which the population is as a maximum. Round to the nearest hour. b. Determine the maximum population. Round to the nearest thousand.The gas mileage mx (in mpg) for a certain vehicle can be approximated mx=0.028x2+2.688x35.012, where x is the speed of the vehicle in mph. a. Determine the speed at which the car gets its maximum gas mileage. b. Determine the maximum gas mileage.The sum of two positive numbers is 24. What two numbers will maximize the product? (See Example 5)The sum of two positive numbers is 1. What two numbers will maximize the product?The difference of two numbers is 10. What two numbers will minimize the product?52PE Suppose that a family wants to fence in an area of their yard for a vegetable garden to keep out deer. One side is already fenced from the neighborâ€™s property. (See Example 5) a. If the family has enough money to buy 160 ft of fencing, what dimensions would produce the maximum area for the garden? b. What is the maximum area?Two chicken coops are to be built adjacent to one another using 120 ft of fencing. a. What dimensions should be used to maximize the area of an individual coop? b. What is the maximum area of an individual coop?A trough at the end of a gutter spout is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminium that is 20 in. long and 12 in. wide. He makes a fold along the two long sides a distance of x inches from the edge. a. Write a function to represent the volume in terms of x. b. What value of x will maximize the volume of water that can be carried by the gutter? c. What is the maximum volume?56PE Tetanus bacillus bacteria are cultured to produce tetanus toxin used in an inactive form for the tetanus vaccine. The amount of toxin produced per batch increases with time and then decrease as the culture becomes unstable. The variable t is the time in hours after the culture has started, and yt is the yield of toxin in grams. (See Example 6) a. Use regression to find a quadratic function to model the data. b. At what time is the yield the greatest? Round to the nearest hour. c. What is the maximum yield? Round to the nearest gram.Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop-and-go traffic. At higher speeds, the car must overcome more wind resistance. The variable x given in the table represents the speed (in mph) for a compact car, and mx represents the gas mileage (in mpg). a. Use regression to find a quadratic function to model the data. b. At what speed is the gas mileage the greatest? Round to the neatest mile per hour. c. What is the maximum gas mileage? Round to the nearest mile per gallon.Fluid runs through a drainage pipe with a 10-cm radius and a length of 30 m (300 cm). The velocity of the fluid gradually decreases from the center of the pipe toward the edges as a result of friction with the walls of the pipe. For the data shown, vx is the velocity of the fluid (in cm/sec) and x represents the distance (in cm) from the center of the pipe toward the edge. a. The pipe is 30 m long (3000 cm). Determine how long it will take fluid to run the length of the pipe through the center of the pipe. Round to 1 decimal place. b. Determine how long it will take fluid at a point 9 cm from the center of the pipe to run the length of Me pipe. Round to 1 decimal place. c. Use regression to find a quadratic function to model the data. d. Use the model from part (c) to predict the velocity of the fluid at a distance 5.5 cm from the center of the pipe. Round tot decimal place.The braking distance required for a car to stop depends on numerous variables such as the speed of the cat, the weight of the car, reaction time of the driver, and the coefficient of friction between the tires and the road. For a certain vehicle on one stretch of highway, the braking distances ds (in ft) are given for several different speeds s (in mph). a. Use regression to find a quadratic function to model the data. b. Use the model from part (a) to predict the stopping distance for the car if it is traveling 62 mph before the brakes are applied. Round to the nearest foot. c. Suppose that the car is traveling 53 mph before the brakes are applied. if a deer is standing in the road at a distance of 245 ft from the point where the brakes are applied. with the car hit the deer?For Exercises 61-64, given a quadratic function defined by fx=ax2+bx+ca0, answer true or false. If an answer is false, explain why. The graph of f can have two y-intercepts.For Exercises 61-64, given a quadratic function defined by fx=ax2+bx+ca0, answer true or false. If an answer is false, explain why. The graph of f can have two x-intercepts.63PE For Exercises 61-64, given a quadratic function defined by fx=ax2+bx+ca0, answer true or false. If an answer is false, explain why. The axis of symmetry of the graph of f is the line defined by y=c.For Exercises 65-70, determine the number of x-intercepts of the graph of fx=ax2+bx+ca0, based on the discriminant of the related equation fx=0 . fx=4x2+12x+9 66PE For Exercises 65-70, determine the number of x-intercepts of the graph of fx=ax2+bx+ca0, based on the discriminant of the related equation fx=0 . fx=x25x+8 For Exercises 65-70, determine the number of x-intercepts of the graph of fx=ax2+bx+ca0, based on the discriminant of the related equation fx=0 . fx=3x2+4x+9 For Exercises 65-70, determine the number of x-intercepts of the graph of fx=ax2+bx+ca0, based on the discriminant of the related equation fx=0 . fx=3x2+6x11 For Exercises 65-70, determine the number of x-intercepts of the graph of fx=ax2+bx+ca0, based on the discriminant of the related equation fx=0 . fx=2x2+5x10 For Exercises 71-78, given a quadratic function defined by fx=axh2+ka0, match the graph with the function based on the conditions given. a0,h0,k0 72PE 73PE For Exercises 71-78, given a quadratic function defined by fx=axh2+ka0, match the graph with the function based on the conditions given. a0,h0,k0 For Exercises 71-78, given a quadratic function defined by fx=axh2+ka0, match the graph with the function based on the conditions given. a0,axisofsymmetryx=2,k0 For Exercises 71-78, given a quadratic function defined by fx=axh2+ka0, match the graph with the function based on the conditions given. a0,axisofsymmetryx=2,k0 For Exercises 71-78, given a quadratic function defined by fx=axh2+ka0, match the graph with the function based on the conditions given. a0,h=2,maximumvalueequals2

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