1. 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. Q2. In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.90 as soon as you get in the taxi, to which a charge of $1.70 per mile is added. Find an equation that can be used to determine the cost, C(x), of an x-mile taxi ride. a. C(x) = 1.70 + 2.90x b. C(x) = 3.10x c. C(x) = 4.60x d. C(x) = 2.90 + 1.70x Q3. 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 Q4. Graph the function h(x) = -2x + 3. State whether it is increasing, decreasing, or constant. a. b. c. d. Q5. 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, ) Q6. Find the domain of the function f(x) = 7 - x. a. {x|x 7} b. {x|x 7} c. {x|x 7} d. {x|x 7} Q7. The graph of a function is given. Decide whether it is even, odd, or neither. a. even b. odd c. neither Q8. 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 Q9. 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 Q10. Determine algebraically whether f(x) = 1/x2 is even, odd, or neither. a. even b. odd c. neither 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. The graph of a function is given. Decide whether it is even, odd, or neither. a. even b. odd c. neither Q13. The graph of a function f is given. Find the numbers, if any, at which f has a local minimum. What are the local minima? a. f has a local minimum at x = -2; the local minimum is 0 b. f has a local minimum at x = 0; the local minimum is 3 c. f has a local minimum at x = -2 and 2; the local minimum is 0 d. f has no local minimum Q14. 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 Q15. 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 Q16. 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 Q17. 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 Q18. 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 Q19. Find (f - g)(4) when f(x) = 5x2 + 6 and g(x) = x + 2. a. 80 b. 88 c. 84 d. -90 Q20. Determine the average rate of change for the function p(x) = -x + 3. a. 3 b. -3 c. -1 d. 1 Q21. Find the domain of the rational function R(x) = (-3x2)/(x2 + 2x - 15). a. {x|x 5, 3} b. {x|x 5, -3} c. {x|x - 15, 1} d. {x|x -5, 3} Q22. 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) Q23. 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 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 Factor Theorem to determine whether x + 5 is a factor of f(x) = 3x3 + 13x2 - 9x + 5. a. Yes b. No Q26. 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 Q27. 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, ) Q28. 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 Q29. 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 Q30. Solve the inequality algebraically. Express the solution in interval notation. x3 27 a. (-, 3] b. (-, -3] [3, ) c. [-3, 3] d. [3, ) Q31. 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} Q32. 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 Q33. 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 Q34. 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 Q35. 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 Q36. Form a polynomial f(x) with real coefficients of degree 3 and the zeros 1 + i and -10. a. f(x) = x3 - 10x2 - 18x - 12 b. f(x) = x3 + 8x2 + 20x - 18 c. f(x) = x3 + x2 - 18x + 20 d. f(x) = x3 + 8x2 - 18x + 20 Q37. Find all zeros of the function f(x) = 2x4 + 3x3 + 16x2 + 27x - 18 and write the polynomial as a product of linear factors. a. f(x) = (2x - 1)(x + 2)(x + 3)(x - 3) b. f(x) = (2x + 1)(x - 2)(x + 3)(x - 3) c. f(x) = (2x - 1)(x + 2)(x + 3i)(x - 3i) d. f(x) = (2x + 1)(x - 2)(x + 3i)(x - 3i) Q38. 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 Q39. 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 Q40. 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 Privacy Policy | Contact