1. Determine the average rate of change for the function p(x) = -x + 3. a. 3 b. -3 c. -1 d. 1 Q2. Find (f - g)(4) when f(x) = 5x2 + 6 and g(x) = x + 2. a. 80 b. 88 c. 84 d. -90 Q3. Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.90. The total cost to regrind 50 platens is $400. Find the linear cost function to regrind platens. If reground platens sell for $8.80 each, how many must be reground and sold to break even? a. C(x) = 1.90x + 305; 45 platens b. C(x) = 1.90x + 400; 38 platens c. C(x) = 1.90x + 400; 58 platens d. C(x) = 1.90x + 305; 29 platens Q4. Graph the function f(x) = -x2 + 3 by starting with the graph of y = x2 and using transformations (shifting, compressing, stretching, and/or reflection). a. b. c. d. Q5. Use the graph to find the intervals on which it is increasing, decreasing, or constant. a. Increasing on (-3, -2) and (2, 4); decreasing on (-1, 1); constant on (-2, -1) and (1, 2) b. Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1); constant on (-2, -1) and (1, 2) c. Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1) d. Decreasing on (-3, -1) and (1, 4); increasing on (-2, 1) Q6. Find the average rate of change for the function f(x) = 3/(x - 2) from the values 4 to 7. a. 7 b. 1/3 c. -3/10 d. 2 Q7. Find -f(x) when f(x) = -2x2 + 5x + 2. a. 2x2 - 5x + 2 b. -2x2 - 5x - 2 c. -2x2 - 5x + 2 d. 2x2 - 5x - 2 Q8. Find the average rate of change for the function f(x) = -3x2 - x from the values 5 to 6. a. 1/2 b. -2 c. -34 d. -1/6 Q9. Determine whether the relation represents a function. If it is a function, state the domain and range. {(-4, 17), (-3, 10), (0, 1), (3, 10), (5, 26)} a. It is a function; domain: {17, 10, 1, 26}; range: {-4, -3, 0, 3, 5} b. It is a function; domain: {-4, -3, 0, 3, 5}; range: {17, 10, 1, 26} c. It is NOT a function. Q10. Determine where the function f(x) = -x2 + 8x - 7 is increasing and where it is decreasing. a. increasing on (4, ) and decreasing on (-, 4) b. increasing on (-, 4) and decreasing on (4, ) c. increasing on (9, ) and decreasing on (-, 9) d. increasing on (-, 9) and decreasing on (9, ) Q11. The graph of a function f is given. Find the numbers, if any, at which f has a local maximum. What are the local maxima? a. f has no local maximum b. f has a local maximum at -; the local maximum is 1 c. f has a local maximum at x = 0; the local maximum is 1 d. f has a local maximum at x = - and ; the local maximum is -1 Q12. Find the vertex and axis of symmetry of the graph of the function f(x) = 3x2 + 36x. a. (-6, -108); x = -6 b. (-6, 0); x = -6 c. (6, -108); x =6 d. (6, 0); x = 6 Q13. The owner of a video store has determined that the profits P of the store are approximately given by P(x) = -x2 + 150x + 50, where x is the number of videos rented daily. Find the maximum profit to the nearest dollar. a. $5675 b. $11,250 c. $5625 d. $11,300 Q14. Graph the function h(x) = -2x + 3. State whether it is increasing, decreasing, or constant. a. b. c. d. Q15. Graph the function f(x) = x2 + 8x + 7 using its vertex, axis of symmetry, and intercepts. a. b. c. d. Q16. The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the interval (-6, -2.5). a. increasing b. decreasing c. constant Q17. Determine, without graphing, whether the quadratic function f(x) = x2 + 2x - 6 has a maximum value or a minimum value and then find that value. a. minimum; -7 b. minimum; -1 c. maximum; -1 d. maximum; -7 Q18. Graph the function F(x) = -5. State whether it is increasing, decreasing, or constant. a. b. c. d. Q19. Determine the slope and y-intercept of the function F(x) = x/4. a. m = 0; b = 1/4 b. m = 1/4; b = 0 c. m = 4; b =0 d. m = -1/4; b = 0 Q20. Match the graph to one of the listed functions. a. f(x) = x2 - 8 b. f(x) = -x2 - 8x c. f(x) = x2 - 8x d. f(x) = -x2 - 8 Q21. Find the x- and y-intercepts of f(x) = (x + 1)(x - 4)(x - 1)2. a. x-intercepts: -1, 1, -4; y-intercept: 4 b. x-intercepts: -1, 1, 4; y-intercept: 4 c. x-intercepts: -1, 1, -4; y-intercept: -4 d. x-intercepts: -1, 1, 4; y-intercept: -4 Q22. Solve the inequality algebraically. Express the solution in interval notation. x3 27 a. (-, 3] b. (-, -3] [3, ) c. [-3, 3] d. [3, ) Q23. Find the real solutions of the equation 3x3 - x2 + 3x - 1 = 0. a. {-3, 1/3, -1} b. {1/3} c. {1/3, -1} d. {-3, -1/3, -1} Q24. Solve the inequality algebraically. Express the solution in interval notation. (x - 6)/(x + 3) > 0 a. (-, -3) (6, ) b. (-, -3) c. (6, ) d. (-3, 6) Q25. The function f(x) = x4 - 5x2 - 36 has the zero -2i. Find the remaining zeros of the function. a. 2i, 6, -6 b. 2i, 3i, -3i c. 2i, 3, -3 d. 2i, 6i, -6i Q26. List the potential rational zeros of the polynomial function f(x) = x 5 - 6x2 + 5x + 15. Do not find the zeros. a. 1, 1/5, 1/3 1/15 b. 1, 5, 3, 15 c. 1, 5, 3 d. 1, 1/5, 1/3, 1/15, 5, 3, 15 Q27. For the polynomial f(x) = (1/5)x(x2 - 5), list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept. a. 0, multiplicity 1, touches x-axis; 5, multiplicity 1, touches x-axis; -5, multiplicity 1, touches x-axis b. 0, multiplicity 1, crosses x-axis; 5, multiplicity 1, crosses x-axis; -5, multiplicity 1, crosses xaxis c. 5, multiplicity 1, touches x-axis; -5, multiplicity 1, touches x-axis d. 0, multiplicity 1 Q28. A polynomial f(x) of degree 3 whose coefficients are real numbers has the zeros -4 and 4 - 5i. Find the remaining zeros of f. a. 4, -4 + 5i b. 4, 4 + 5i c. 4 + 5i d. -4 + 5i Q29. Find a bound on the real zeros of the polynomial function f(x) = x4 - 8x2 - 9. a. -17 and 17 b. -9 and 9 c. -18 and 18 d. -10 and 10 Q30. Solve the inequality algebraically. Express the solution in interval notation. (9x - 5)/(x + 2) 8 a. (-2, 13] b. (-2, 21) c. (-2, 21] d. (-2, 13) Q31. Find the intercepts of the function f(x) = x2(x - 1)(x - 6). a. x-intercepts: 0, -1, -6; y-intercept: 0 b. x-intercepts: 0, 1, 6; y-intercept: 6 c. x-intercepts: 0, 1, 6; y-intercept: 0 d. x-intercepts: 0, -1, -6; y-intercept: 6 Q32. Solve the inequality algebraically. Express the solution in interval notation. (x - 2)2(x + 9) < 0 a. (-, -9) or (9, ) b. (-, -9] c. (-, -9) d. (-9, ) Q33. Give the equation of the horizontal asymptote, if any, of the function f(x) = (x 2 - 5)/ (25x - x4). a. y = -1 b. no horizontal asymptotes c. y = 0 d. y = -5, y = 5 Q34. State whether the function f(x) = x(x -7) is a polynomial function or not. If it is, give its degree. If it is not, tell why not. a. Yes; degree 2 b. No; x is raised to non-integer power c. Yes; degree 1 d. No; it is a product Q35. Find the intercepts of the function f(x) = x3 + 3x2 - 4x - 12. a. x-intercepts: -2, 2, 3; y-intercept: -12 b. x-intercepts: -3, -2, 2; y-intercept: -12 c. x-intercept: -3; y-intercept: -12 d. x-intercept: -2; y-intercept: -12 Q36. Use the graph to find the vertical asymptotes, if any, of the function. a. none b. x = -2 c. y = -2 d. x = -2, x = 0 Q37. Find the intercepts of the function f(x) = 4x5(x + 3)3. a. x-intercepts: 0, -3; y-intercept: 0 b. x-intercepts: 0, 3; y-intercept: 4 c. x-intercepts: 0, 3; y-intercept: 0 d. x-intercepts: 0, -3; y-intercept: 4 Q38. Find the domain of the rational function f(x) = (x + 9)/(x2 - 4x). a. {x|x -2, x 2} b. {x|x -2, x 2, x -9} c. all real numbers d. {x|x 0, x 4} Q39. Form a polynomial f(x) with real coefficients of degree 4 and the zeros 2i and -5i. a. f(x) = x4 + 29x2 + 100 b. f(x) = x4 - 2x3 + 29x2 + 100 c. f(x) = x4 + 29x2 - 5x + 100 d. f(x) = x4 - 5x2 + 100 Q40. Use the Factor Theorem to determine whether x + 5 is a factor of f(x) = 3x3 + 13x2 - 9x + 5. a. Yes b. No