Name Class Date Precalculus Unit 2 Practice

NameclassdatePrecalculus Unit 2 PracticeLesson 9-11. Examine the data in the table. What type of function could be used to model the data? Explain your reasoning.University of ber ofEnrolled Students(in thousands)1010.51215.620.121.222.72530.532.85. Data are collected on puppies and their growth(by weight) over a 6-month period. What type offunction could be used to model the data for theweight as a function of the number of months sincethe birth of a puppy? Explain your reasoning.2. Model with mathematics. Use the regressioncapabilities of your graphing calculator to find amodel that best represents the data in Item 1.3. Attend to precision. Graph the equation youfound in Item 2. List the important features ofthe graph. Approximate any values to threedecimal places.Lesson 9-2y504540353025201510506. Which of the following functions is a fifth degreepolynomial?A. f(x) 5 x(x 2 3)2(x 1 2)B. f(x) 5 x2 1 2x(x 1 5)(x 2 7)0 1 2 3 4 5 6 7 8 9 10C. f(x) 5 (x 2 1)(x 1 9)3(x 2 2)xD. f(x) 5 x5(x 2 11)4. Use the regression model to predict about howmany students will be attending University XYZ in2020.A. 34,000B. 36,000C. 38,000D. 2,899,000 2015 College Board. All rights reserved.1SpringBoard Precalculus, Unit 2 Pratice

NameclassdateLesson 10-17. Make use of structure. List the important featuresof the graph below. Approximate any values tothree decimal places. ake use of structure. For Items 11 and 12, determineMthe y-intercept and the end behavior of each function.y11. f(x) 5 7x7 2 8x5 1 3x4 1 2x2 215412. h(x) 5 4(x 2 1)2(x 2 3)(x 1 2)32125242322121234513. What are the zeros of the functionf(x) 5 (x 1 2)4(x 2 3)5?x21A. x 5 2, 2322B. x 5 22, 323C. x 5 4, 524D. x 5 24, 252514. Attend to precision. Factor and find the zeros ofthe function.g(m) 5 m4 2 2m3 1 8m 2168. Without using a calculator, determine the endbehavior and x- and y-intercepts of the functionf (x) 5 (2x 2 1)(x 1 1)(x 1 3).15. Graph f(x) 5 (x 2 1)(x 1 5)2.f(x)9. Without using a calculator, find the end behavior,maximum possible zeros, and maximum possibleturning points of the function f (x) 5 x6 2 2x3 1 1.x10. Use appropriate tools strategically. Use agraphing calculator to find the zeros, turningpoints, y-intercepts, and end behavior.y 5 2x5 1 5.7x4 2 8x3 2 15x2 1 28 2015 College Board. All rights reserved.2SpringBoard Precalculus, Unit 2 Pratice

NameclassdateLesson 10-2Lesson 10-316. Which of the following are possible zeros off(x) 5 3x4 1 x2 2 8?8A. 633B. 621C. 6216D. 6321. Which function has the greatest number of signchanges?A. f(x) 5 x7 2 10x6 1 40x5 2 96x4 1 176x3 2224x2 2128x 2 1B. g(x) 5 x7 2 10x6 2 40x5 2 96x4 1 176x3 2224x2 2128x 2 1C. h(x) 5 x7 1 10x6 1 40x5 2 96x4 2 176x3 1224x2 2128x 1 1D. j(x) 5 x7 1 10x6 1 40x5 1 96x4 1 176x3 1224x2 1128x 2 117. Use the Rational Root Theorem to find the possiblereal zeros and the Factor Theorem to find the zerosof the function.Make use of structure. For Items 22 and 23, determinethe number of positive and negative real zeros.u(t) 5 3t3 2 5t2 1 6t 1 822. f(x) 5 2120x5 2 146x4 2 x3 1 27x2 1 x 2 123. f(x) 5 2150x3 1 153x 1 90Make use of structure. For Items 18 and 19, use theRational Root Theorem and synthetic division to findthe real zeros.Attend to precision. For Items 24 and 25, sketch agraph of the polynomial function.18. f(x) 5 35x3 2 114x2 1 25x 1 624. f(x) 5 x3 2 3x2 1 3x 21f(x)19. g(x) 5 4x4 2 65x2 1 16x20. Use appropriate tools strategically. Use theRational Root Theorem and a graphing calculatorto find the rational root(s) of the polynomial.f(x) 5 x4 2 5x 1 4 2015 College Board. All rights reserved.3SpringBoard Precalculus, Unit 2 Pratice

Nameclassdateb. Sketch and label a graph of the volume function.25. f(x) 5 2x4 2 3x3 2 2x2 1 3x 1 1f(x)f(x)xx28. Use a graphing calculator to find the maximumvolume of a box that the Orange Cell PhoneCompany can make. What are the dimensions ofthe box with a maximum volume, and what is itsvolume?Lesson 11-1Orange Cell Phone Company is creating a package fortheir newest phone. The box package is made fromcardboard pieces that are 14 inches long by 5 incheswide. The boxes are made by cutting a section of size xby x out of each corner of the cardboard.29. Which polynomial has degree 6 and zeros1 3x 5 26 2 1, 0, , 1, ?2 226. Model with mathematics. Write the equation thatrepresents the volume of the box.A. f (x) 5 (x 2 1)2(x 2 3)(x 1 1)(x 1 6)13B. f (x) 5 x x 1 (x 1 1) x 1 (x 2 1)(x 2 6)22( )( )C. f (x) 5 x(2x 11)(x 1 1)(2x 1 3)(x 2 1)(x 2 6)D. f (x) 5 x(2x 21)(x 2 1)(2x 2 3)(x 1 1) (x 1 6)27. a. Determine the possible domain and range forthe construction of these boxes.30. Make use of structure. Find a polynomial with realcoefficients of given degree with the given zeros.degree: 4; zeros: x 5 21, 0, 3, 10 2015 College Board. All rights reserved.4SpringBoard Precalculus, Unit 2 Pratice

Nameclass37. Use a graphing calculator to determine the intervalover which the volume of the frame boxes madefrom the pieces of metal is larger than 28 cubic feet.Lesson 11-231. Which of the following is a factor of the functionf (x) 5 2x2 2 8?A. x 1 8B. x 2 4C. x 2 2D. 2x 2 2date38. Use appropriate tools strategically. Using thepiece of metal, what are the dimensions of the airconditioner with the largest possible volume?Make use of structure. For Items 32 and 33, rewrite eachpolynomial function as a product of complex factors.32. f (x) 5 x2 1 144A. 1.7 feet by 4.6 feet by 5.8 feetB. 2 feet by 8 feet by 15 feetC. 2 feet by 4 feet by 3.5 feetD. 1.7 feet by 7.5 feet by 8 feet33. g(x) 5 3x4 2 4x 2 7Solve each inequality and write the solution interval.39. x2 2 5x , 6Attend to precision. For Items 34 and 35, find thezeros of each function.34. h (x) 5 x2 2 2x 1 340. x4 32435. r (x) 5 x4 1 27xLesson 12-1Model with mathematics. Student A and Student B arestudying for the same test at the same rate. Bothstudents studied through the dinner hour. Right now,Student B has been studying twice as many hours afterthe dinner hour as Student A. When both studentsstudy 1 more hour, Student B will have studied one anda half times as many hours from the dinner hour asStudent A.Lesson 11-3Model with mathematics. MetalBox Manufacturingalso makes industrial air conditioning frames from an8-foot-by-15-foot piece of metal. Square corners oflength x are cut from each piece. The volume of theframe box must be at least 28 cubic feet.Let h represent Student A’s number of hours studiedsince the dinner hour.36. Write an inequality for the volume that satisfies theconstraint.41. Which equation can be used to find h, the currentnumber of hours Student A has been studying?A. h 5 h 1 1 B. h 1 1 5 1.5(h 1 1)C. 2h 5 2h 1 1 2015 College Board. All rights reserved.5D. 2h 1 1 5 1.5(h 1 1)SpringBoard Precalculus, Unit 2 Pratice

Nameclass42. Find the number of hours Student A has studiedright now since the dinner hour.date47. Find the equation of the vertical asymptote of O(x).A. x 5 1B. x 5 2143. Let S(x) represent the ratio of Student A’s numberof hours studied since the dinner hour to StudentB’s number of hours studied since the dinner hour,and let x represent the number of hours from now,either past or future. Write S as a function of x.C. x 5 13D. x 5 21348. Find the equation of the horizontal asymptoteof O(x).A. y 5 144. What appears to happen to the ratio of Student A’snumber of hours since the dinner hour to StudentB’s number of hours since the dinner hour as xincreases?B. y 5 21C. y 5 10D. y 5 21345. Reason abstractly. If the two students keepstudying at the same rate forever, would Student Aever catch up to Student B? Explain.49. Demonstrate why the value of O(x) will neveractually reach the value of the horizontalasymptote.Lesson 12-210 1 xrepresents13 1 xthe ratio of Amy’s age in years to Michael’s age in years,where x represents the number of years from now,either past or future.Model with mathematics. O(x) 550. Use appropriate tools strategically. Use agraphing calculator to look at the behavior of theO(x) to the left of the vertical asymptote. Explainwhy you are not looking at that part of the graphfor the given scenario.46. Sketch a graph of the function O(x)for 215 , x , 15.yyxx 2015 College Board. All rights reserved.6SpringBoard Precalculus, Unit 2 Pratice

NameclassLesson 13-153. u(x) 51151. Consider the graphs for f(x) 5 and g(x) 5.x 25xWhich of the following best describes thedifference between the graphs of the two functions?date26 122xyA. g(x) is a shift of f(x) to the left 5 units.B. g(x) is a shift of f(x) to the right 5 units.C. g(x) is a shift of f(x) up 5 units.D. g(x) is a shift of f(x) down 5 units.xFor Items 52 and 53, sketch a graph of each function.152. h(x) 55x 1 3y54. Attend to precision. Write to explain to another1student how to obtain the graph of r(x) 511x 111from the graph of f(x) 5 .xx55. Express regularity in repeated reasoning. Writeto explain to another student the similarities in the1graphs of m(x) 51 b, n(x) 5 (x 1 a)2 1 b,x 1aand o(x) 5 x 1 a 1 b when compared to thegraphs of their respective parent functions. 2015 College Board. All rights reserved.7SpringBoard Precalculus, Unit 2 Pratice

NameclassLesson 13-2date60. Attend to precision. Sketch a graph of thefunction without using a graphing calculator.3x 1 4p(x) 5 3x 214 x 22156. What is the horizontal asymptote of f(x) 5 2 ?3x 12A. y 5 01B. y 524C. y 533D. y 54yx57. What is the horizontal asymptote of7 x 2 6 x 4 1 3x 2?g(x) 5 39 x 2 x 11 2 4 x 4A. y 5 0793C. y 521D. y 53B. y 5Lesson 13-3Model with mathematics. For Items 61–63, write apossible function whose graph could have the followingasymptotes.61. y 5 24, x 5 358. Make use of structure. Find the equation of theslant asymptote of the function.5 x 2 2 3 x 11h(x) 5x 2162. y 5 0, x 5 6159. Find the vertical asymptote and the pointdiscontinuity in the graph of the function.x 2 2 2x 1 3f (x) 5x 4 2 81 2015 College Board. All rights reserved.163. y 5 2 x 1 1, x 5 028SpringBoard Precalculus, Unit 2 Pratice

Nameclass65. Critique the reasoning of others. Kayla says thata function that is a rational expression has onlyvertical asymptotes where the factors in thedenominator equal zero. Is she correct? If not,explain and correct her error.64. Which of the following functions could have apoint of discontinuity at x 5 1?xA. f(x) 5x 21x 21B. f(x) 5( x 21)( x 11)x 11C. f(x) 5( x 11)( x 21)x2D. f(x) 5x 21 2015 College Board. All rights reserved.date9SpringBoard Precalculus, Unit 2 Pratice

5 Name class date 2015 College Board. All rights reserved. SpringBoard Precalculus, Unit 2 Pratice LeSSon 11-2 31. Which of the following is a factor of the function