1. Solve the equation log a. {-7} 4 (x + 2) = -1 b. {-7/4} c. {9/4} d. {9} Q2. Use the horizontal line test to determine whether the function is one-to-one. a. Yes b. No Q3. The half-life of silicon-32 is 710 years. If 100 grams is present now, how much will be present in 200 years? (Round your answer to three decimal places.) a. 14.192 b. 82.263 c. 98.066 d. 0 Q4. Write log 2 (7m 3n)/k2 as the sum and/or difference of logarithms. Express powers as factors. a. (1/7) log 2 m + (1/3) log 2 n - 2log 2 k b. (1/7) log 2 m (1/3) log 2 n 2log 2 k c. 7log 2 m + 3log d. (7/2) log 2 2 n - 2log m + (3/2) log 2 2 k n - (2/2) log 2 k Q5. Find the amount that results from the investment of $12,000 invested at 5% compounded quarterly after a period of 8 years. a. $5857.57 b. $17,729.47 c. $17,857.57 d. $17,637.10 Q6. For the functions f(x) = x2 + 4 and g(x) = x2 + 1, find the composite function (f g)(x). a. x4 + 5 b. x4 + 17 c. x4 + 2x2 + 5 d. x4 + 8x2 + 17 Q7. If 5x = 6,what does 5-2x equal? a. 1/36 b. 36 c. 1/12 d. -36 Q8. Find the domain of the composite function f g if f(x) = 28/x and g(x) = -8/(x - 7). a. {x | x 7} b. {x | x 0, x 7, x 4} c. {x | x 7, x 0} d. {x | x is any real number} Q9. The graph of a one-to-one function f(x) = x + 2 is given. Draw the graph of the inverse function f-1 as a dashed line or curve. a. b. Q10. Write log 7 (xy)/15 as the sum and/or difference of logarithms. Express powers as factors. a. (1/2) log 7 xy - (1/2) log 7 15 b. (1/2) log 7 x (1/2) log c. (1/2) log 7 x + (1/2) log d. (1/2) log 7 x + (1/2) log 7 y (1/2) log 7 15 7 y - (1/2) log 7 15 7 y - log 7 15 Q11. The graph of an exponential function is given. Match the graph to one of the following functions. a. f(x) = 3x b. f(x) = -3x c. f(x) = 3-x d. f(x) = -3-x Q12. Find functions f and g so that f g = H(x) = (5 - 2x3)2. a. f(x) = 5 - 2x3 ; g(x) = x2 b. f(x) = (5 - 2x)3 ; g(x) = x2 c. f(x) = x2 ; g(x) = 5 - 2x3 d. f(x) = x3 ; g(x) = (5 - 2x)2 Q13. A thermometer reading 8C is brought into a room with a constant temperature of 20C. If the thermometer reads 18C after 5 minutes, what will it read after being in the room for 7 minutes? Assume the cooling follows Newton's Law of Cooling: U = T + (U o T)ekt. (Round your answer to two decimal places.) a. 1.6C b. 20.98C c. 19.02C d. 20C Q14. Change the exponential expression 5-3 = 1/125 to an equivalent expression involving a logarithm. a. log -3 1/125 = 5 b. log 5 1/125 = -3 c. log 5 -3 = 1/125 d. log 1/125 5 = -3 Q15. Solve the equation (1/3) log a. {9} 2 (x + 6) = log 8 (3x). b. {3, 0} c. {3} d. Q16. Find the present value to get $6500 after 2 years at 5% compounded quarterly. Round to the nearest cent. a. $5895.69 b. $614.91 c. $5885.09 d. $5958.65 Q17. Solve the equation log a. {-6} 4 (x + 4) + log 4 (x - 2) = 2 b. {4} c. {4, -6} d. {5} Q18. Solve the equation 3x = 81. a. {27} b. {5} c. {4} d. {3} Q19. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described. a. f -1(x) = (x - 20)/2 b. f -1(x) = x - 20 c. f -1(x) = (x/2) - 20 d. f -1(x) = (x/2) + 20 Q20. Find the exact value of the logarithmic expression log a. -1/3 4 1/64. b. -3 c. 1/3 d. 3 Q21. Solve the system of equations using substitution. a. x = -6, y = 7; x = -7, y = 6 or (-6, 7), (-7, 6) b. x = -6, y = -7; x = -7, y = -6 or (-6, -7), (-7, -6) c. x = 6, y = -7; x = 7, y = -6 or (6, -7), (7, -6) d. x = 6, y = 7; x = 7, y = 6 or (6, 7), (7, 6) Q22. Graph the solution set of the system of inequalities or indicate that the system has no solution. a. b. c. d. Q23. a. b. c. d. Q24. Solve the system of equations using Cramer's Rule if it is applicable. a. x = -4, y = 3; (-4, 3) b. x = -3, y = -4; (-3, -4) c. x = 4, y = 3; (4, 3) d. x = 3, y = 4; (3, 4) Q25. Find the value of the determinant. a. 224 b. 24 c. -72 d. 72 Q26. Solve the system of equations by substitution. a. x = 2, y = 9; (2, 9) b. x = 3, y = 9; (3, 9) c. x = 3, y = 8; (3, 8) d. x = 2, y = 8; (2, 8) Q27. Use properties of determinants to find the value of the second determinant, if the value of the first is known. a. 9 b. -18 c. 18 d. -9 Q28. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1. a. minimum: 7 b. minimum: 18 c. minimum: 24 d. minimum: 13 Q29. Find the inverse of the matrix. Be sure to check your answer. a. b. c. d. Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. a. x = 2, y = 3, z = -7; (2, 3, -7) b. x = 1, y = 3, z = -4; (1, 3, -4) c. x = 5, y = 13/2, z = -3; (5, 13/2, -3) d. x = 1, y = -3, z = -16; (1, -3, -16) Q31. Solve using elimination. a. x = 5, y = 9; x = -5, y = 9; x = 5, y = -9; x = -5, y = -9 or (5, 9), (-5, 9), (5, -9), (-5, -9) b. x = 5, y = 9; x = 9, y = 5; x = -5, y = -9; x = -9, y = -5 or (5, 9), (9, -5), (-5, -9), (-9, -5) c. x = -5, y = -9; x = -9, y = -5 or (-5, -9), (-9, -5) d. x = 5, y = -9; x = 5, y = 9 or (5, -9), (5, 9) Q32. Solve the system of equations using substitution. a. x = 2, y = 4; x = 2, y = -4; x = -2, y = 0 or (2, 4), (2, -4), (-2, 0) b. x = 2, y = 4; x = -2, y = 0 or (2, 4), (-2, 0) c. x = 2, y = 4; x = 2, y = -4 or (2, 4), (2, -4) d. x = 2, y = 4 or (2, 4) Q33. Write the partial fraction decomposition of the rational expression (4x 3 + 4x2)/(x2 + 5)2. a. (4x - 4)/(x2 + 5) + (-20x + 20)/(x2 + 5)2 b. (4x + 4)/(x2 + 5) + (-20x - 20)/(x2 + 5)2 c. (4x + 4)/(x2 + 5) + (20x - 20)/(x2 + 5)2 d. (4x + 4)/(x2 + 5) + (20x + 20)/(x2 + 5)2 Q34. Write the partial fraction decomposition of the rational expression (125 - 19x)/(x 3 10x2 + 25x). a. 5/x + -5/(x - 5) + 12/(x - 5)2 b. -5/x + 5/(x - 5) + 6/(x - 5)2 c. 5/x + 6/(x - 5) + -5/(x - 5)2 d. 5/x + -5/(x - 5) + 6/(x - 5)2 Q35. Solve the system of equations. a. x = -4, y = 4, z = -3; (-4, 4, -3) b. x = -3, y = 4, z = -4; (-3, 4, -4) c. x = -4, y = -3, z = 4; (-4, -3, 4) d. inconsistent Q36. Write a system of linear inequalities that has the given graph. a. b. c. d. Q37. Graph the inequality x + y < -5. a. b. c. d. Q38. A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for $0.25 and an ounce of potatoes for $0.03. Let x = the number of ounces of chicken and y = the number of ounces of potatoes purchased per patient. Write the objective function that describes the total cost per patient per meal. a. z = 3y + 25y b. z = 0.25x + 0.03y c. z = 25x + 3y d. z = 0.03x + 0.25y Q39. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. a. x = -2, y = -1, z = 0; (-2, -1, 0) b. x = -2, y = 0, z = -1; (-2, 0, -1) c. x = 0, y = -2, z = -1; (0, -2, -1) d. x = 0, y = -1, z = -2; (0, -1, -2) Q40. The perimeter of a rectangle is 20 inches and its area is 21 square inches. What are its dimensions? a. 2 in. by 6 in. b. 3 in. by 7 in. c. 4 in. by 6 in. d. 2 in. by 8 in