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| Q1. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1. [removed] a. -3 [removed] b. -2 [removed] c. 3 [removed] d. 2 Q2. Solve the inequality. (x – 5)(x2 + x + 1) > 0 [removed] b. (-1, 1) [removed] c. (-∞, 5) [removed] d. (5, ∞) Q3. Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval. f(x) = 8x3 – 10x2 + 3x + 5; [-1, 0] [removed] b. f(-1) = -16 and f(0) = 5; yes [removed] c. f(-1) = 16 and f(0) = -5; yes [removed] d. f(-1) = 16 and f(0) = 5; no Q4. Solve the equation in the real number system. x4 – 3x3 + 5x2 – x – 10 = 0 [removed] b. {1, 2} [removed] c. {-1, 2} [removed] d. {-2, 1} Q5. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = x2 – 2x – 5 [removed] b. minimum; 1 [removed] c. maximum; – 6 [removed] d. minimum; – 6 Q6. Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither. f(x) = [removed] b. symmetry with respect to the y-axis [removed] c. neither Q7. Find the domain of the rational function. f(x) = [removed] b. {x|x ≠ 3, x ≠ -5} [removed] c. all real numbers [removed] d. {x|x ≠ 3, x ≠ -3, x ≠ -5} Q8. Find the domain of the rational function. g(x) = [removed] b. {x|x ≠ -7, x ≠ 7, x ≠ -5} [removed] c. {x|x ≠ -7, x ≠ 7} [removed] d. {x|x ≠ 0, x ≠ -49} Q9. Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = 3x4 + 4x3 + 13x2 + 16x + 4 [removed] b. f(x) = (3x + 1)(x + 1)(x + 2i)(x – 2i) [removed] c. f(x) = (3x – 1)(x – 1)(x + 2i)(x – 2i) [removed] d. f(x) = (3x + 1)(x + 1)(x + 2)(x – 2) Q10. Use the graph to find the vertical asymptotes, if any, of the function.
[removed] b. x = 0, y = 0 [removed] c. x = 0 [removed] d. none Q11. Find the power function that the graph of f resembles for large values of |x|. f(x) = (x + 5)2 [removed] b. y = x25 [removed] c. y = x2 [removed] d. y = x5 Q12. Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither. f(x) = [removed] b. symmetry with respect to the origin [removed] c. neither Q13. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = -x2 – 2x + 2 [removed] b. maximum; 3 [removed] c. minimum; 3 [removed] d. maximum; – 1 Q14. Find the power function that the graph of f resembles for large values of |x|. f(x) = -x2(x + 4)3(x2 – 1) [removed] b. y = -x7 [removed] c. y = x3 [removed] d. y = x2 Q15. A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 320 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? [removed] a. 25,600 ft2 [removed] b. 19,200 ft2 [removed] c. 12,800 ft2 [removed] d. 6400 ft2 Q16. Find the indicated intercept(s) of the graph of the function. x-intercepts of f(x) = [removed] b.  [removed] c.  [removed] d. (-5, 0) Q17. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. f(x) = 9x3 + 8x2 – 6 [removed] b. Yes; degree 5 [removed] c. Yes; degree 3 [removed] d. Yes; degree 6 Q18. Solve the equation in the real number system. x3 + 9x2 + 26x + 24 = 0 [removed] b. {2, 4} [removed] c. {3, 2, 4} [removed] d. {-4, -2} Q19. Use the graph to find the vertical asymptotes, if any, of the function.
[removed] b. x = -3, x = 3, y = 0 [removed] c. none [removed] d. x = -3, x = 3 Q20. Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval. f(x) = -2x4 + 2x2 + 4; [-2, -1] [removed] b. f(-2) = -20 and f(-1) = 4; yes [removed] c. f(-2) = 20 and f(-1) = -4; yes [removed] d. f(-2) = -20 and f(-1) = -4; no |
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