Question 1

Which of the following is NOT a polynomial function?

Accepted Answer

$$p(x) = \frac{1}{x} + 2$$

Question 2

What is the degree of the polynomial $$f(x) = 4x^5$ - 2x^3$ + x - 7$$?

Accepted Answer

$$5$$

Question 3

Given the polynomial $$f(x) = (x-2)(x+3)(x-5)$$, what are its real zeros?

Accepted Answer

$$x = 2, -3, 5$$

Question 4

If $$f(x) = (x-1)^2$(x+4)$$, what is the multiplicity of the zero at $$x=1$$?

Accepted Answer

$$2$$

Question 5

A polynomial function of degree $$n$$ can have at most how many turning points?

Accepted Answer

$$n-1$$

Question 6

Describe the end behavior of $$f(x) = -2x^4$ + 5x^2$ - 3 as$$ $$x 	o \infty.$$

Accepted Answer

$$f(x) 	o -\infty$$

Question 7

What is the domain of the rational function $$R(x) = \frac{x^2$ - 3}{x^2$ + 2x - 8}$$?

Accepted Answer

$$x 
eq -4, 2$$

Question 8

Which of the following describes the vertical asymptotes of $$f(x) = \frac{2x}{x^2$ - 9}$$?

Accepted Answer

$$x = 3, x = -3$$

Question 9

For the rational function $$f(x) = \frac{3x^2$ + 1}{x^2$ - 4}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 3$$

Question 10

Solve the inequality $$\frac{x-3}{x+2} \u003e 0.$$

Accepted Answer

$$x \u003e 3 or$$ $$x \u003c -2$$

Question 11

Use synthetic division to find the remainder when $$f(x) = 2x^3$ - 3x^2$ - 14x + 15 is $$divided by $$x-3.$$

Accepted Answer

$$-6$$

Question 12

According to the Rational Zeros Theorem, what are the possible rational zeros of $$f(x) = 2x^3$ - 3x^2$ + 4$$?

Accepted Answer

$$\pm1, \pm2, \pm4, \pm\frac{1}{2}, \pm\frac{2}{2}, \pm\frac{4}{2}$$

Question 13

If $$f(x) = x^4$ + 2x^2$ + 1$$, how many real zeros can $$f(x)$$ have at most?

Accepted Answer

$$4$$

Question 14

Which theorem guarantees that a polynomial function with real coefficients and odd degree has at least one real zero?

Accepted Answer

A polynomial of odd degree has at least one real zero

Question 15

Given $$f(x) = x^3$ - 2x^2$ - x + 2$$, use the Factor Theorem to determine if $$x-1 is a $$factor.

Accepted Answer

No, because $$f(1) 
eq 0$$

Question 16

If $$f(x) = x^2$ + 4$$, what are the complex zeros?

Accepted Answer

$$x = 2i, x = -2i$$

Question 17

A rational function $$R(x) = \frac{p(x)}{q(x)}$$ has a vertical asymptote at $$x=2$$ with even multiplicity. What does the graph do near $$x=2$$?

Accepted Answer

It approaches the same infinity on both sides of $$x=2$$

Question 18

Which of the following is true about the graph of $$f(x) = x^3$ - 3x^2$ + 2x$$?

Accepted Answer

It has at most 2 turning points

Question 19

If $$f(x) = x^4$ + 2x^2$ + 1$$, what is the end behavior as $$x 	o -\infty$$?

Accepted Answer

$$f(x) 	o \infty$$

Polynomial and Rational Functions: Graphs, Properties, and Zeros

Study Guide - Practice Questions