MAC 1140 Spring 2014 Final Exam

MAC 1140 Spring 2014 Final Exam Section # _ Name _ UFID# _ Signature _ A. Sign your scantron on the back at the bottom in ink. B. In pencil, write and encode on your scantron in the spaces indicated: 1) Name (last name, first initial, middle initial) 2) UF ID Number 3) Section Number C. Under "special codes", code in the test ID number 5, 1. 1 2 3 4 6 7 8 9 0 2 3 4 5 6 7 8 9 0 D. At the top right of your answer sheet, for "Test Form Code", encode A. BCD E E. 1) There are twenty-three 5-point multiple choice questions 115-points. 2) The time allowed is 120 minutes. 3) You may write on the test. 4) Raise your hand if you need more scratch paper or if you have a problem with your test. DO NOT LEAVE YOUR SEAT UNLESS YOU ARE FINISHED WITH THE TEST. F. KEEP YOUR SCANTRON COVERED AT ALL TIMES. G. When you are finished: 1) Before turning in your test, check for transcribing errors. Any mistakes you leave in are there to stay. 2) Bring your test, scratch paper, and scantron to your proctor to turn them in. Be prepared to show your UF ID card. 3) Score will be posted in Sakai within a few days. The Honor Pledge: "On my honor, I have neither given nor received unauthorized aid in doing this exam." Student's Signature: _

.' Questions 1-23 are worth 5 points each. 6x-7) X2-1. Find the domain of f(x) = In ( x _ 7. A. (-1,00) D. (-1,7) B. (-00,1) E. (-1,7) U (7,00) C. [-1,00) 2. The function f(x) = log3(2x + 1) - 3 is one-to-one. Find its inverse function. A. f-l(x) = log3 ex;-l) B. f-l(x) = e3x+3-1 C f-1(x) 1. log3(2x + 1) - 3 3 x+3 1 D. f-l(x) = - 2 E. f-l(x) = 3~ 3. Simplify completely: (xy)2 _ (_y)6 y2(y2 _ x)(x + y2) A. -1 B. 0 C. X+y2 E. 1 4. Find the equation of a line that contains (-1, 1) and is perpendicular to the line 2x+ 3y = 7. A. y = ~x + ~ D. y = ~x + ~ B. y = -;2X + 7 E. y = lx + ~ 2 2 1A

1. 5. Let f(x) = 2" and g(x) = v'x + 2. Find the domain of (f 0 g)(x). x A. [-2,00) B. (-2,00) C. (-00, -2) U (-2,00) D. (-00,0) U (0, -2) U (-2,00) E. (-00,00) 6. Let f(x) = 2x+1 and g(x) = log2(x) + 3. Find (f 0 g)(x). A. (f 0 g)(x) = x D. (f 0 g)(x) = 16x B. (fog)(x)=x+4 E. (f 0 g)(x) = e2x c. (f 0 g)(x) = x +3... f(x+h)-f(x). 7. Let f(x) = X~1. Fmd and simplify h ' given h -=I O. A. }],_1 x- B. (X!1)2 C. h D -1. (x-1)(x+h-1) E. ~ 8. A polynomial f(x) has degree 3 and a leading coefficientof 6. Which of the following are true? a. f(x) must have at least one real root. b. The graph of f(x) rises to the right. c. The graph of f(x) has a horizontal asymptote. A. b only B. a and b only C. a and conly D. band conly E. a, b, and c 2A

9. Represent 'The distance between x and -1 is at least 12' using absolute values. A. Ix - 11 2::12 D. Ix - 121 < 1 B. Ix - 121 2::-1 E. Ix+ 11 S; 12 C. Ix+ll2:: 12 10. Completely factor and write without negative exponents: X-1/2(X-8)3/2_4x1/2(X-8)-1/2 6 (x - 16)(x - 4) (x - 8)2 A. (x(x _ 8))1/2 B. C. X1/2(X - 8)1/2 X1/2(X - 8)1/2 D. x2-20x + 64 E. (X+8)1/2+1+4x X1/2 /" 11. Let f(x) = x3-3x2 + kx + 7. Find a value for k such that x + 1 is a factor of f(x). A. 1 B. -2 C. -3 D. 2 E. 3 12. Suppose a population model is given by y = 2+3~~"17t. What is the initial population? A.5 B. 1+ e C. 4 D. 25 E 25." 2+3e "13. Choose the interval that contains all of the solutions to 2 x 14 x + 1 + x - 2 = x2 - X - 2' A. (-3,00) D. (1,6) B. [-6,3] C. (-1,6) E. None of the above 3A

14. Find the inverse function f(x) = 4x-1 + 3.. A. f-l(x) = logx(~)+ 1 B. f-l(x) = {/(x + 1) - 3 C. f-l(x) = log4(x + 1) - 3 D. f-l(x) = log3(x - 4) + 1 E. f-l(x) = log4(x - 3) + 1 15. Write.: -. in standard form. 2-'/, 1. A. "2-'/, l+i D. 3 E. 1+ 2i 16. Let f(x) = (tx - 1//X + \). Which of the followingare true? x-3 x-6 a. The graph of f(x) has a horizontal asymptote at y = 2. b. The graph of f(x) has an x-intercept at x = 1/2. c. The graph of f(x) has an x-intercept at x = 6. A. a only D. band conly B. a and b only C. a and conly E. a, band c 17. Solve the system of equations 2x - 3y = 1 -x+4y = 7. Find the sum of x and y. A. 5 D.7 B. -6 C. 8 E. There is no solution. 4A

18. Consider the function f(x) = In(x - 1) + 2. Which of the following are true? a. The graph of f(x) has a horizontal asymptote at y = 2. b. The graph of f(x) has a vertical asymptote at x = 1. c. The domain of f(x) is (-00,1) U (1, (0). A. a only D. a and b only B. b only C. conly E. band conly 19. Combine the following into a single logarithm. 12log(x) + 6log(y) -log(x2) A. log(x10y6) D. log Cx~r8) B. X log(y6) E. 16log(xy) 20. Find all real solutions to the equation A. x=o D. x = log3(25) - 7 E. There is no solution. 25 B. x = «r C. x = log3(25) 7 21. Bonus: An interest-baring account is compounded continuously at an annual rate of 5%. If the initial amount in the account is $450, what equation below gives the account balance after t years? A. A = 5e4,50t B. A = 450(1.05Y D. A = 450e,05t E. A = 150e,05t C. A = 450e5t 5A

c,' 22. Bonus: Solve the equation and simplify the solution A. x = log8(18)- B. x = 2log3 e:) - 1 c - log3(18). x - 1+21og3(5) - log3(18) E. x - 21og3(5) 23. Bonus: Which interval below contains. all the solutions to the equation In(x + 5) = In(x - 1) + In(x + 1) A. [-4,-2] B. [-4, -3] c. [-5, -3] D. [1,3] E. [-2,1] 6A

MAC 1140 Spring 2014 Final Exam Section # _ Name _ UFID# _ Signature _ A. Sign your scantron on the back at the bottom in ink. B. In pencil, write and encode on your scantron in the spaces indicated: 1) Name (last name, first initial, middle initial) 2) UF ID Number 3) Section Number C. Under "special codes", code in the test ID number 5, 2. 1 2 3 4 6 7 8 9 0 1.34 5 6 7 8 9 0 D. At the top right of your answer sheet, for "Test Form Code", encode B. A C D E E. 1) There are twenty-three 5-point multiple choice questions 115-points. 2) The time allowed is 120 minutes. 3) You may write on the test. 4) Raise your hand if you need more scratch paper or if you have a problem with your test. DO NOT LEAVE YOUR SEAT UNLESS YOU ARE FINISHED WITH THE TEST. F. KEEP YOUR SCANTRON COVERED AT ALL TIMES. G. When you are finished: 1) Before turning in your test, check for transcribing errors. Any mistakes you leave in are there to stay. 2) Bring your test, scratch paper, and scantron to your proctor to turn them in. Be prepared to show your UF ID card. 3) Score will be posted in Sakai within a few days. The Honor Pledge: "On my honor, I have neither given nor received unauthorized doing this exam." aid in Student's Signature: _

Questions 1-23 are worth 5 points each. 1. Simplify completely: (xy)2 _ (_y)6 y2(y2 _ X)(X + y2) A. X+y2 B. X2 Y C. 1 D. -1 E. 0 2. Write _i - in standard form. 2-i 1+i A. 3 1. B. '2-1, D. 1+ 2i 3. Let f(x) = ~x - l//x + 1/. Which of the following are true? x-3 x-6 a. The graph of f(x) has a horizontal asymptote at y = 2. b. The graph of f(x) has an z-intercept at x = 1/2. c. The graph of f(x) has an x-intercept at x = 6. A. a only D. band conly B. a and b only C. a and conly E. a, band c 4. Solve the system of equations 2x - 3y = 1 -x+4y = 7. Find the sum of x and y. A.8 D.7 B. 5 C. -6 E. There is no solution. IB

5. Consider the function f(x) = In(x - 1) + 2. Which of the following are true? a. The graph of f(x) has a horizontal asymptote at y = 2. b. The graph of f(x) has a vertical asymptote at x = 1. c. The domain of f(x) is (-00,1) U (1,00). A. a only D. a and b only B. b only C. conly E. band conly 6. Find the equation of a line that contains (-1, 1) and is perpendicular to the line 2x + 3y = 7. A. y = -.}x + 7 D. Y = Ix +!! 2 2 B. y = 32X + ~ E. y = ~x+ ~ C - 3 + 5. Y -"2x "2 7. The functionf(x) = log3(2x + 1) - 3 is one-to-one. Find its inverse function. -1( ) _ 1 A. f x - log3(2x + 1) - 3 3 x+3 1 B f-l(x) = ---. 2 C. f-l(x) = 3xt3 D. f-l(x) = log, ex;-1) E. f-l(x) = e3x+3-1 2B

o. MAC 1140 - Spring 2014 - Final Exam 8. Combine the following into a single logarithm. 12log(x) + 6Iog(y) - log(x2) B. log ( (x~r8 ) C. 16Iog(xy) E. log(x6y6) 9. Find all real solutions to the equation A. x=o B x = log3(25). 7 25 C. X = e'r D. x = log3(25) - 7 E. There is no solution. 1 10. Let f(x) = """2 and g(x) = Vx + 2. Find the domain of (J 0 g)(x). x A. [-2,(0) B. (-00, -2) U (-2,00) C. (-00,0) U (0, -2) U (-2,00) D. (-2,00) E. (-00,00) 11. Let f(x) = 2x+l and g(x) = log2(x) + 3. Find (J 0 g)(x). A. (J 0 g)(x) = x D. (J o.g)(x) = x + 4 B. (J 0 g)(x) = 16x E. (Jog)(x)=x+3 C. (J 0 g)(x) = e2x 38

12. Let f(x) = X~I' Find and simplify f(x + h~- f(x), given h =f O. A. h B. h x-i D -1. (x-l)(x+h-l) E. k C. (X!I)2 13. A polynomial f(x) has degree 3 and a leading coefficient of 6. Which of the following are true? a. f(x) must have at least one real root. b. The graph of f(x) rises to the right. c. The graph of f(x) has a horizontal asymptote. A. b only B. a and b only C. a and conly D. band conly E. a, b, and c 14. Represent 'The distance between x and -1 is at least 12' using absolute values. A. \x -12\ < 1 D. \x-12\2:-1 B. \x+1\::; 12 E. \x+ 1\2: 12 C. \x - 1\ 2: 12.15. Completely factor and write without negative exponents: x-1/2(x_8)3/2_4x1/2(x_8)-1/2 (x - 8)2 A. X1/2(X _ 8)1/2 (x + 8)1/2 + 1+ 4x D. X1/2 B. x2-20x + 64 6 E. (x(x _ 8))1/2 C (x - 16)(x - 4). X1/2(X - 8)1/2 16. Let f(x) = x3-3x2 + kx + 7. Find a value for k such that x + 1 is a factor of f(x). A.l B. 3 C. -2 D. -3 E. 2 4B

17. Find the inverse function f(x) = 4x-1 + 3. A. f-l(x) = log3(x- 4) + 1 B. f-l(x) = log4(x- 3) + 1 C. f-l(x) = logx(~)+ 1 D. f-l(x) = (l{x + 1) - 3 E. f-l(x) = log4(x+ 1) - 3 X2-6x - 7) 18. Find the domain of f (x) = In. ( x-7 A. (-1,00) D. (-1,7) B. (-00,1) E. (-1,7) U (7,(0) C. [-1,(0) 19. Suppose a population model is given by y = 2+3:5.17t. What is the initial population? A.5 B 25. 2+3e C. 1 +e D.4 E.25 20. Choose the interval that contains all of the solutions to 2 x 14 --+--=. x + 1 x - 2 x2 - X - 2 A. (-3, (0) D. (1,6) B. (-1,6) C. [-6,3] E. None of the above 21. Bonus: An interest-baring account is compounded continuously at an annual rate of 5%. If the initial amount in the account is $450, what equation below gives the account balance after t years? A. A = 450e5t B. A = 450e 05t C. A = 5e4.50t D. A = 450(1.05)t E. A = 150e o5t 58

22. Bonus: Solve the equation and simplify the solution 3x52x = 18. - log3(18) A. x - 1+21og3(5) B. x = log8(18) c. x = 2log3 en - 1 D. x = log3(18) - 1-2log3(5) E x = log3(18). 21og3(5) 23. Bonus: Which interval below contains all the solutions to the equation In(x + 5) = In(x - 1) + In(x + 1) A. [-5, -3] B. [1,3] c. [-4,-3] D: [-2,1] E. [-4, -2] 68