Question 1

Which of the following is the set of critical values for the function $$f(x) = x^3$ - 6x^2$ + 17x - 6$$?

Accepted Answer

$$x = 6, 17; (-6, -9); (17, -9)$$

Question 2

Solve the equation $$3x^2 - 2x + 8 = 0$.

Accepted Answer

$$x = [-1, 1]$$

Question 3

State the domain of the rational function $$f(x) = \frac{2x^2$ - 5x + 12}{x^2$ - 2x - 8}.$$

Accepted Answer

$$(-\infty, -2) \cup (-2, 4) \cup (4, \infty)$$

Question 4

Find the vertical asymptote(s) of the graph of $$f(x) = \frac{2x^2$ - 5x + 12}{x^2$ - 2x - 8}.$$

Accepted Answer

$$x = -2, x = 4$$

Question 5

Find the horizontal asymptote, if any, of the rational function $$f(x) = \frac{5x^2$ - 2x + 8}{x^2$ - 2x - 8}.$$

Accepted Answer

$$y = 1$$

Question 6

Find the oblique asymptote, if any, of the rational function $$f(x) = \frac{2x^2$ - 5x + 12}{x^2$ - 2x - 8}.$$

Accepted Answer

None

Question 7

Find a polynomial function of degree 3 with $$-1, 2, 4 as $$zeros.

Accepted Answer

$$f(x) = x^3$ - 5x^2$ + 10x - 8$$

Question 8

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros: $$2, 4 + 2\sqrt{2}, 4 - 2\sqrt{2}.$$

Accepted Answer

$$f(x) = (x - 2)(x^2$ - 8x + 12)$$

Question 9

Given the graph of $$y = 2x^2$ - 3x - 2$$, which of the following correctly describes its intercepts?

Accepted Answer

x-intercept $$(-2, 0)$$, y-intercept $$(0, 1)$$

Question 10

Given that the polynomial function $$f(x) = x^3$ - 8x^2$ - 17x - 36$$ has the zero $$x = 1 + \sqrt{5}$$, find the other zeros.

Accepted Answer

$$1 - \sqrt{5}, -1, -2$$

Question 11

Give all possible rational zeros for the polynomial $$f(x) = x^3$ - 8x^2$ + 8x - 224.$$

Accepted Answer

$$\pm 1, \pm 2, \pm 4, \pm 8, \pm 16, \pm 28, \pm 56, \pm 112, \pm 224$$

Question 12

How many positive and negative real zeros does the polynomial $$f(x) = x^4$ + 2x^3$ + 2x^2$ + 8$$ have?

Accepted Answer

0 positive, 1 or 2 negative

Question 13

Use synthetic division to find the function value for $$f(x) = x^3$ - 3x^2$ + 6x - 3 at$$ $$x = 5.$$

Accepted Answer

$$67$$

Question 14

Which graph best represents the function $$f(x) = 2x^3$ + 2(x - 1)$$?

Accepted Answer

C

Question 15

Find the correct end behavior diagram for the polynomial function $$f(x) = x^3$ - 3x^2$ - 2x + 5.$$

Accepted Answer

$$\downarrow, \downarrow$$

Question 16

Find the zeros of the polynomial function $$f(x) = x^3$ - 6x^2$ + 8$$ and state the multiplicity of each.

Accepted Answer

$$2$$, multiplicity 1; 1, multiplicity 2$

Question 17

Find the zeros of the polynomial function $$f(x) = x^4$ - 6x^2$ + 8$$ and state the multiplicity of each.

Accepted Answer

$$2$$, multiplicity 1; -2, multiplicity 1; \sqrt{2}, multiplicity 1; -\sqrt{2}, multiplicity 1$

College Algebra: Rational and Polynomial Functions Study Guide

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