Q1. 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

Q2. 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, )

Q3. Find (f - g)(4) when f(x) = 5x² + 6 and g(x) = x + 2.

a. 80

b. 88

c. 84

d. -90

Q4. 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.

Q5. Graph the function h(x) = -2x + 3. State whether it is increasing, decreasing, or constant.

a.

b.

c.

d.

Q6. The graph of a function is given. Decide whether it is even, odd, or neither.

a. even

b. odd

c. neither

Q7. 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

Q8. Determine algebraically whether f(x) = 1/x² is even, odd, or neither.

a. even

b. odd

c. neither

Q9. The graph of a function is given. Decide whether it is even, odd, or neither.

a. even

b. odd

c. neither

Q10. Determine algebraically whether f(x) = -2x³ is even, odd, or neither.

a. even

b. odd

c. neither

Q11. 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

Q12. Graph the function f(x) = x² + 8x + 7 using its vertex, axis of symmetry, and intercepts.

a.

b.

c.

d.

Q13. 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)

Q14. 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

Q15. 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

Q16. 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

Q17. 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

Q18. 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

Q19. 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

Q20. 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

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. 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

Q23. 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

Q24. 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

Q25. 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

Q26. 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

Q27. Use the Factor Theorem to determine whether x + 5 is a factor of f(x) = 3x³ + 13x² - 9x + 5.

a. Yes

b. No

Q28. 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)

Q29. 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}

Q30. Use transformations of the graph of y = x⁴ to graph the function f(x) = 5x⁴.

a.

b.

c.

d.

Q31. Find the x-intercepts of the graph of the function f(x) = (x - 3)(2x + 7)/(x² + 9x - 8).

a. (3, 0), (-7, 0)

b. (-3, 0), (7/2, 0)

c. (3, 0), (-7/2, 0)

d. none

Q32. 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

Q33. 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}

Q34. 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 x-axis

c. 5, multiplicity 1, touches x-axis; -5, multiplicity 1, touches x-axis

d. 0, multiplicity 1

Q35. Solve the inequality algebraically. Express the solution in interval notation.

x³ 27

a. (-, 3]

b. (-, -3] [3, )

c. [-3, 3]

d. [3, )

Q36. 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}

Q37. 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)

Q38. 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

Q39. 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

Q40. 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