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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