Exam practice Disclaimer. The actual test does not mirror this practice. This is meant as a means to help you understand the material.

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1 Eam 3 24 practice Disclaimer. The actual test does not mirror this practice. This is meant as a means to help ou understand the material. Graph the function. 1) f() = ) Sketch the graph of the rational function. 2) f() = 4 ( + 4)( + 2) 2) 1

2 Identif an vertical, horizontal, or oblique asmptotes in the graph of = f(). State the domain of f. 3) 3) A) Vertical: = -3; horizontal: = 0; (-, -3) (-3, ) B) Vertical: = -3; horizontal: = 0; (-, 0) (0, ) C) Vertical: = 0; horizontal: = -3; (-, -3) (-3, ) D) Vertical: = 0; horizontal: = -3; (-, 0) (0, ) Use snthetic division to perform the division. 4) ) Give the equation of the oblique asmptote, if an. ) f() = ) Use snthetic division to perform the division. 6) ) Give the equation of the oblique asmptote, if an. 7) f() = ) Use snthetic division to perform the division. 8) 8) ) ) 2

3 Use the remainder theorem and snthetic division to find f(k). ) k = 4 + i; f() = 3 + ) Solve the problem. Round to the nearest tenth unless indicated otherwise. 11) The volume of a gas varies inversel as the pressure and directl as the temperature (in degrees Kelvin). If a certain gas occupies a volume of 2. liters at a temperature of 380 K and a pressure of 20 newtons per square centimeter, find the volume when the temperature is 46 K and the pressure is 30 newtons per square centimeter. 11) Use the remainder theorem and snthetic division to find f(k). 12) k = i; f() = ) Use snthetic division to perform the division. 13) ) Solve the problem. 14) The weight that a horizontal beam can support varies inversel as the length of the beam. Suppose that a -m beam can support 730 kg. How man kilograms can a -m beam support? 14) 1) The current I in an electrical conductor varies inversel as the resistance R of the conductor. The current is amperes when the resistance is 719 ohms. What is the current when the resistance is 420 ohms? Round to the nearest tenth. 1) Solve the problem. Round to the nearest tenth unless indicated otherwise. 16) The cost of stainless steel tubing varies jointl as the length and the diameter of the tubing. If a foot length with diameter 2 inches costs $48.00, how much will a 11 foot length with diameter inches cost? Round to the nearest cent. 16) Use snthetic division to decide whether the given number k is a zero of the given polnomial function. 17) 2 ; f() = ) Use the remainder theorem and snthetic division to find f(k). 18) k = -2; f() = ) Epress f() in the form f() = ( - k)q() + r for the given value of k. 19) f() = ; k = -3 19) 20) f() = ; k = -1 20) Use snthetic division to decide whether the given number k is a zero of the given polnomial function. 21) 2 + i; f() = ) 3

4 Find all comple zeros of the polnomial function. Give eact values. List multiple zeros as necessar. 22) f() = ) 23) f() = ) 24) f() = ) Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. 2) = 0 2) Find a polnomial of lowest degree with onl real coefficients and having the given zeros. 26) 4 + 6, 4-6, and 3 26) 27) 2, -8, and 3 + 4i 27) Solve the problem. Round our answer to two decimal places. 28) The area of a circle varies directl as the square of the radius of the circle. If a circle with a radius of inches has an area of 78. square inches, what is the area of a circle with a radius of 20 inches? 28) 29) The distance to the horizon varies directl as the square root of the height above ground level of the observer. If a person can see 6 miles from a height of 2 feet, how far can a person see from a height of 49 feet? 29) 30) The weight W of an object on the Moon varies directl as the weight E on earth. A person who weighs 18 lb on earth weighs 31.6 lb on the Moon. How much would a 12-lb person weigh on the Moon? 30) Find a polnomial of lowest degree with onl real coefficients and having the given zeros. 31) 1-3, 1 + 3, and 1 + i 31) Find the zeros of the polnomial function and state the multiplicit of each. 32) f() = ( ) 2 32) Find all rational zeros and factor f(). 33) f() = ) 34) f() = ) 3) f() = ) Use the remainder theorem and snthetic division to find f(k). 36) k = -3; f() = ) 4

5 Find the zeros of the polnomial function and state the multiplicit of each. 37) ( - 7) 3 ( 2-16) 37) Use snthetic division to decide whether the given number k is a zero of the given polnomial function. 38) - - 4i; f() = ) Use the remainder theorem and snthetic division to find f(k). 39) k = -3; f() = ) Use snthetic division to decide whether the given number k is a zero of the given polnomial function. 40) -2; f() = ) Use the remainder theorem and snthetic division to find f(k). 41) k = 2 + i; f() = ) Use the factor theorem to decide whether or not the second polnomial is a factor of the first. 42) ; + 42) Use snthetic division to decide whether the given number k is a zero of the given polnomial function. 43) 7i; f() = ) For the function as defined that is one-to-one, graph f and f-1 on the same aes. 44) f() = ) Use snthetic division to decide whether the given number k is a zero of the given polnomial function. 4) 1 2 ; f() = ) Factor f() into linear factors given that k is a zero of f(). 46) f() = 3 - (4 + 2i)2 + (- + 8i) + i; k = 2i 46)

6 For the function as defined that is one-to-one, graph f and f-1 on the same aes. 47) f() = ) Factor f() into linear factors given that k is a zero of f(). 48) f() = ; k = ) Use the factor theorem to decide whether or not the second polnomial is a factor of the first. 49) ; ) The graph of a function f is given. Use the graph to find the indicated value. 0) f-1(3) 8 0) Use snthetic division to decide whether the given number k is a zero of the given polnomial function. 1) 3i; f() = ) 6

7 For the function as defined that is one-to-one, graph f and f-1 on the same aes. 2) f() = 7 2) For the polnomial, one zero is given. Find all others. 3) P() = ; -3 3) Use the factor theorem to decide whether or not the second polnomial is a factor of the first. 4) ; - 2 4) Find the domain and range of the inverse of the given function. ) f() = - 9 ) Give all possible rational zeros for the following polnomial. 6) P() = ) Factor f() into linear factors given that k is a zero of f(). 7) f() = ; k = 6 7) Give all possible rational zeros for the following polnomial. 8) P() = ) Find all rational zeros and factor f(). 9) f() = ) Factor f() into linear factors given that k is a zero of f(). 60) f() = ; k = -4 (multiplicit 2) 60) 7

8 For the polnomial, one zero is given. Find all others. 61) P() = ; -4 61) Find the domain and range of the inverse of the given function. 62) f() = 7-2 ; 0 62) Give all possible rational zeros for the following polnomial. 63) P() = ) Find the zeros of the polnomial function and state the multiplicit of each. 64) ( - 7) 3 ( 2-4) 64) Find all rational zeros and factor f(). 6) f() = ) Find the zeros of the polnomial function and state the multiplicit of each. 66) f() = 3( + 6) 2 ( - 6) 3 66) Find a polnomial of lowest degree with onl real coefficients and having the given zeros. 67) 3 + 3, 3-3, and 3 67) 68) - 7, 7, and -3i 68) Find the future value. 69) $481 invested for 4 ears at 4% compounded annuall 69) Solve the equation. 70) e - 1 = 1 e ) 71) m-4 = ) Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. 72) = 0 72) 73) = 0 73) 8

9 Find all comple zeros of the polnomial function. Give eact values. List multiple zeros as necessar. 74) f() = ) Find the zeros of the polnomial function and state the multiplicit of each. 7) ) Find the equation that the given graph represents. 76) 76) A) P() = B) P() = C) P() = D) P() = Find the future value. 77) $ invested for 11 ears at 4% compounded monthl 77) Solve the problem. 78) Find the required annual interest rate, to the nearest tenth of a percent, for $1113 to grow to $1830 if interest is compounded quarterl for ears. 78) Sketch the graph of the polnomial function. Label at least two points on the graph. 79) f() = )

10 80) f() = -( + 2) 4 80) Find the equation that the given graph represents. 81) 81) A) P() = B) P() = C) P() = D) P() = Find all comple zeros of the polnomial function. Give eact values. List multiple zeros as necessar. 82) f() = ) Find a polnomial of lowest degree with onl real coefficients and having the given zeros. 83) 8, -14, and 3 + 8i 83) Solve the problem. 84) Find the required annual interest rate, to the nearest tenth of a percent, for $168 to grow to $47 if interest is compounded weekl for ears. Assume eactl 2 weeks per ear. 84)

11 Answer the question. 8) How man positive real zeros does this graph have? 8) Solve the problem. 86) If varies inversel as 2, and = 6 when = 8, find when = 4. 86) 87) If f varies jointl as q 2 and h, and f = 144 when q = 4 and h = 3, find q when f = 72 and h = 6. 87) Determine whether or not the function is one-to-one. Give reason for answer. 88) 88) - - Find the horizontal asmptote of the given function. 89) h() = ) Solve the problem. 90) If m varies directl as and, and m = 24 when = 6 and = 9, find m when = 1 and = 8. 90) Give the domain and range for the rational function. Use interval notation. 91) f() = 1 ( - 2) ) 11

12 Use the graph to answer the question. 92) Find the horizontal and vertical asmptotes of the rational function graphed below. 92) Solve the problem. 93) A() = gives the alcohol level in an average person's blood hrs after drinking 8 oz of 0-proof whiske. If the level eceeds 1. units, a person is legall drunk. Would a person be drunk after 2 hours? 93) Use the boundedness theorem to determine whether the statement is true or false. 94) The polnomial f() = has no real zero greater than 3. 94) Use the intermediate value theorem for polnomials to show that the polnomial function has a real zero between the numbers given. 9) f() = ; -1 and 0 9) Find the correct end behavior diagram for the given polnomial function. 96) P() = ) Find a polnomial of degree 3 with real coefficients that satisfies the given conditions. 97) Zeros of -3, 2, 4 and P(1) = 12 97) 98) Zeros of -2, 1, 0 and P(2) = 40 98) Find the correct end behavior diagram for the given polnomial function. 99) P() = ) Find a polnomial of lowest degree with onl real coefficients and having the given zeros. 0) 6 + 2i and 6-2i 0) Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. 1) = 0 1) 12

13 2) = 0 2) Find all comple zeros of the polnomial function. Give eact values. List multiple zeros as necessar. 3) f() = ) Sketch the graph of the polnomial function. 4) f() = 3-2 Label at least two points on the graph. 4) ) f() = Label at least two point on the graph. ) Find the correct end behavior diagram for the given polnomial function. 6) P() = ) 13

14 Graph the polnomial function. Factor first if the epression is not in factored form. 7) f() = 2( + 2)( - 1) Label at least two points on the graph. 7) Use the intermediate value theorem for polnomials to show that the polnomial function has a real zero between the numbers given. 8) f() = ; -2 and -1 8) Use the boundedness theorem to determine whether the statement is true or false. 9) The polnomial f() = has no real zero greater than 8. 9) Give the domain and range for the rational function. Use interval notation. 1) f() = ) Find an vertical asmptotes. 111) h() = ( - )( + 2) ) Find the horizontal asmptote of the given function. 112) f() = ) 14

15 Sketch the graph of the rational function. 113) f() = - 4 Label at least two points on the graph and draw an asmptotes. 113) + Solve the problem. Round our answer to two decimal places. 114) The period of vibration P for a pendulum varies directl as the square root of the length L. If the period of vibration is 4. sec when the length is 81 inches, what is the period when L =.062 inches? 114) Solve the problem. 11) The weight of a bod above the surface of the earth is inversel proportional to the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied b 3? 11) Determine whether or not the function is one-to-one. Give a reason for our answer. 116) 116) If f is one-to-one, find an equation for its inverse. 117) f() = ) 1

16 118) f() = ) Determine whether or not the function is one-to-one. 119) f() = ) 120) f() = ) If f is one-to-one, find an equation for its inverse. 121) f() = ) 122) f() = ) Decide whether or not the functions are inverses of each other. 123) f() = , domain [0, ); g() = - 2, domain [2, ) 123) 6 124) f() = 1, g() = ) 12) )

17 Answer Ke Testname: 24 3_2T4_1EXAMP 1) ) ) A 4) ) = + 6 6) ) = ) ) ) i 11) 2.0 liters 12) -11-3i 13) ) 36 kg 1) 8.6 amperes 16) $ ) No 18) ) f() = ( + 3)( ) ) f() = ( + 1)( ) ) No 22) -2i, 2i, 6, -6 23) 3, - 3i, 3i, ) -2i, 2i, 7, -7 17

18 Answer Ke Testname: 24 3_2T4_1EXAMP 2) Positive (3, 1), negative (0) 26) f() = ) f() = ) 126 square inches 29) 8.4 miles 30) 2 lb 31) f() = ) -, multiplicit 2; -9, multiplicit 2 33) 1 2, 1, -2; f() = (2-1)(4-1)( + 2) 4 34) - 1 2, 1, -6; f() = (2 + 1)( - 1)( + 6) 3) - 1 3, 1, -; f() = (3 + 1)(4-1)( + ) 4 36) ) Multiplicit 1 : 0 Multiplicit 1 : ±4 Multiplicit 3 : 7 38) Yes 39) ) Yes 41) i 42) Yes 43) Yes 44) ) Yes 46) f() = ( - 2i)( + 1)( - ) 18

19 Answer Ke Testname: 24 3_2T4_1EXAMP 47) ) (3-1)(2 + 3)( + ) 49) No 0) 2 3 1) Yes 2) Function is its own inverse 3) 3 + 2i, 3-2i 4) No ) Domain: [0, ); range: [9, ) 6) ±1, ±23, ±1/2, ± 23/2 7) ( - 6)( - 2)( + 6) 8) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24 9) 1 2, - 1, 7; f() = (2-1)(2 + 1)( - 7) 2 60) f() = ( + 4)2( - 8) 61) 3 + 2i, 3-2i 62) Domain: (-, 7]; range: range: [0, ) 63) ±1, ±1/2, ±2, ±4, ±8 64) Multiplicit 1 : 0 Multiplicit 1 : ±2 Multiplicit 3 : 7 6) 3, 6, -1; f() = ( - 3)( - 6)( + 1) 19

20 Answer Ke Testname: 24 3_2T4_1EXAMP 66) -6, multiplicit 2; 6, multiplicit 3 67) f() = ) f() = ) $ ) ) -3, 3 72) Positive (1), negative (3, 1) 73) Positive (4, 2, 0), negative (0) 74) 6, - 6i, 6i, - 6 7) Multiplicit : 0 Multiplicit 1 : (±1/4)i 76) A 77) $ ).1% 79) ) ) A 82) -2i, 2i,, - 83) f() = ) 11.8% 8) 2 86) 24 87) 2 20

21 Answer Ke Testname: 24 3_2T4_1EXAMP 88) Yes 89) = 2 90) ) Domain: (-, 2) (2, ); Range: (1, ) 92) Horizontal: = -1; vertical: = ±4 93) Yes 94) True 9) f(-1) = and f(0) = -7 96) 97) P() = ) P() = ) 0) ) Positive (2, 0), negative (1) 2) Positive (3, 1), negative (0) 3) 6, 1 + 2i, 1-2i 4) ) ) 21

22 Answer Ke Testname: 24 3_2T4_1EXAMP 7) ) f(-2) = -7 and f(-1) = 11 9) False 1) Domain: (-, 0) (0, ); Range: (-, 3) (3, ) 111) = 1, = ) = 1 113) ) 1.12 sec 11) The weight is divided b ) No 117) f-1() = ) f-1() = ) Yes 120) No 121) f -1 () = ) f -1 () = ) Yes 124) No 12) No 22

Test # 2 Review Sections (2.4,2.5,2.6, & ch. 3) Math 1314 Name

Test # 2 Review Sections (2.4,2.5,2.6, & ch. 3) Math 1314 Name Test # Review Sections (.,.,., & ch. 3) Math 131 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the equation of the line. 1) -intercept,