$f(x) = a(x + 2)(x - 3)(x + 1)$, where $a \neq 0$

$f(x) \to +\infty$ as $x \to \pm\infty$

Question 1

Which of the following functions is a polynomial function?

Accepted Answer

$f(x) = 3x - 1 - 2x^5$

Question 2

What is the degree of the polynomial $h(x) = x^{12} + 3x^2 - 10x$?

Accepted Answer

$12$

Question 3

Given the polynomial $f(x) = 2(x + 3)^2(x + 2)^3(x - 5)$, what is the multiplicity of the zero at $x = 2$?

Accepted Answer

$3$

Question 4

For the polynomial $f(x) = -6(x - 3)^2(x + 3)^3(x - 4)$, what is the end behavior as $x 	o -\infty$?

Accepted Answer

$f(x) 	o +\infty$

Question 5

Which of the following is the standard form of the polynomial $h(x) = 4x^2 - 5x + 2x - 4$?

Accepted Answer

$h(x) = 4x^2 - 3x - 4$

Question 6

What is the domain of the rational function $f(x) = \frac{1}{x^2 - 2x - 8}$?

Accepted Answer

$x 
eq 2, x 
eq -4$

Question 7

If a polynomial function has degree $n$, what is the greatest number of turning points it can have?

Accepted Answer

$n - 1$

Question 8

Given the polynomial $f(x) = x^3(x - 2)^2(x + 1)$, which zero will the graph touch but not cross the x-axis?

Accepted Answer

$x = 2$

Question 9

Which of the following describes the end behavior of $f(x) = -2x^5 + 3x^2 - x$ as $x 	o +\infty$?

Accepted Answer

$f(x) 	o -\infty$

Question 10

Which of the following is NOT a property of polynomial functions?

Accepted Answer

The graph can have holes or gaps.

Question 11

Find the domain of the rational function $f(x) = \frac{x^2}{x^2 + 1}$.

Accepted Answer

All real numbers

Question 12

Given the zeros $-2, 3, -1$ and degree $3$, which of the following is a possible polynomial function?

Accepted Answer

$f(x) = a(x + 2)(x - 3)(x + 1)$, where $a 
eq 0$

Question 13

For the rational function $f(x) = \frac{x - 2}{x^2 + 3x - 10}$, which value is NOT in the domain?

Accepted Answer

$x = -5$

Question 14

If $f(x) = a_nx^n + \ldots + a_0$ and $a_n > 0$, $n$ is even, what is the end behavior of $f(x)$?

Accepted Answer

$f(x) 	o +\infty$ as $x 	o \pm\infty$

Question 15

Which of the following is the correct definition of a rational function?

Accepted Answer

A function that can be written as $f(x) = \frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomials and $q(x) 
eq 0$.

Question 16

If $f(x) = (x - 1)^3(x + 2)^2$, what is the degree of the polynomial?

Accepted Answer

$5$

Question 17

Which of the following describes the behavior of the graph at a zero with even multiplicity?

Accepted Answer

The graph touches the x-axis and turns around.

Question 18

Given the polynomial $f(x) = 2x^4(x - 1)(x + 5)$, what is the leading term?

Accepted Answer

$2x^6$

Question 19

Which of the following is the constant term in the polynomial $f(x) = 3x^4 - 2x^2 + 7x - 5$?

Accepted Answer

$-5$

Polynomial and Rational Functions: Definitions, Properties, and Graphing

Study Guide - Practice Questions