Q1. 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 Q2. 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 Q3. Graph the function h(x) = -2x + 3. State whether it is increasing, decreasing, or constant. a. b. c. d. Q4. Graph the function F(x) = -5. State whether it is increasing, decreasing, or constant. a. b. c. d. Q5. 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. Q6. 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 Q7. Graph the function f(x) = x² + 8x + 7 using its vertex, axis of symmetry, and intercepts. a. b. c. d. Q8. For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. a. Absolute maximum: f(4) = 7; Absolute minimum: f(1) = 2 b. Absolute maximum: f(4) = 7; Absolute minimum: none c. Absolute maximum: none; Absolute minimum: none d. Absolute maximum: none; Absolute minimum: f(1) = 2 Q9. 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 Q10. 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 Q11. Determine algebraically whether f(x) = 1/x² is even, odd, or neither. a. even b. odd c. neither Q12. 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 Q13. Find the vertex and axis of symmetry of the graph of the function f(x) = x² - 10x. a. (-5, 25); x = -5 b. (25, -5); x = 25 c. (-25, 5); x = -25 d. (5, -25); x = 5 Q14. 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 Q15. The graph of a function is given. Decide whether it is even, odd, or neither. a. even b. odd c. neither Q16. 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 Q17. Determine the average rate of change for the function p(x) = -x + 3. a. 3 b. -3 c. -1 d. 1 Q18. Find (f - g)(4) when f(x) = 5x² + 6 and g(x) = x + 2. a. 80 b. 88 c. 84 d. -90 Q19. For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. a. Absolute maximum: f(-1) = 6; Absolute minimum: f(1) = 2 b. Absolute maximum: f(3) = 5; Absolute minimum: f(1) = 2 c. Absolute maximum: none; Absolute minimum: none d. Absolute maximum: none; Absolute minimum: f(1) = 2 Q20. 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, ) 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. (x - 2)²(x + 9) < 0 a. (-, -9) or (9, ) b. (-, -9] c. (-, -9) d. (-9, ) Q23. Solve the inequality algebraically. Express the solution in interval notation. x³ 27 a. (-, 3] b. (-, -3] [3, ) c. [-3, 3] d. [3, ) Q24. Find the power function that the graph of f(x) = (x + 4)² resembles for large values of |x|. a. y = x⁸ b. y = x² c. y = x⁴ d. y = x¹⁶ Q25. 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 Q26. Find the real solutions of the equation x⁴ - 8x³ + 16x² + 8x - 17 = 0. a. {-1, 1} b. {-1, 4} c. {-4, 4} d. {-4, 1} Q27. List the potential rational zeros of the polynomial function f(x) = x⁵ - 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 Q28. For the polynomial f(x) = 4(x - 5)(x - 6)³, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept. a. 5, multiplicity 1, touches x-axis; 6, multiplicity 3 b. -5, multiplicity 1, touches x-axis; -6, multiplicity 3 c. 5, multiplicity 1, crosses x-axis; 6, multiplicity 3, crosses x-axis d. -5, multiplicity 1, crosses x-axis; -6, multiplicity 3, crosses x-axis Q29. Give the equation of the horizontal asymptote, if any, of the function f(x) = (x² - 5)/(25x - x⁴). a. y = -1 b. no horizontal asymptotes c. y = 0 d. y = -5, y = 5 Q30. 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 Q31. 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 Q32. 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) Q33. 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 Q34. State whether the function f(x) = x(x - 9) 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; it is a product c. Yes; degree 0 d. Yes; degree 1 Q35. Use the Intermediate Value Theorem to determine whether the polynomial function f(x) = -4x⁴ - 9x² + 4; has a zero in the interval [-1, 0]. a. f(-1) = -9 and f(0) = -4; no b. f(-1) = 9 and f(0) = 5; no c. f(-1) = 9 and f(0) = -4; yes d. f(-1) = -9 and f(0) = 4; yes Q36. 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 Q37. 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 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. 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 Q40. Use transformations of the graph of y = x⁴ to graph the function f(x) = 5x⁴. a. b. c. d.