Algebra and Trigonometry

See the attached file for full problem description.

16. The figure shows the graphs of f(x) = x^3 and g(x) = ax^3. What can you conclude about the value of a?

a. a < -1
b. -1 < a < 0
c. 0 < a < 1
d. 1 < a

17. If f(x) = x(x+1)(x=4), use interval notation to give all values of x where f(x) > 0.

a. (-1, 4)
b. (-1, 0) U (4, infinity)
c. (-1, 4)
d. (0, 1) U (4, infinity)

18. Find the third degree polynomial whose graph is shown in the figure.

a. f(x) = x^3 - x^2 - x + 5
b. f(x) 1/25(x^3) - 1/5(x^2) - x + 5
c. f(x) = 1/25(x^3) - 1/5(x^2) + 5x + 5
d. f(x) = 1/5(x^3) + 1/5(x^2) - x + 5

19. The figure shows the graph of the polynomial function y = f(x).

For which of the values k = -2, 1, 2, or 3 will the equation f(x) = k have distinct real roots.

a. -2
b. 1
c. 2
d. 3

20. The degree three polynomial f(x) with real coefficients and leading coefficent 1, has -3 and +4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.

a. f(x) = (x+3)(x^2 + 16)
b. f(x) = (x+3)(x^2 + 8x + 16)
c. f(x) = (x+3)(X^2 - 8x + 16)
d. f(x) = (x-3)(x^2 + 16)

21. For the function f(x) shown in problem 1, find the domain and range of f^-1(x).

a. Domain = [0, 6], Range [1, 4]
b. Domain = [0, 4], Range [1, 6]
c. Domain = [1, 4], Range [0, 6]
d. Domain = [1, 6], Range [0, 4]

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