Question 1

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

Accepted Answer

$$f(x) = \frac{p(x)}{q(x)}$$, where $$p(x)$$ and $$q(x)$$ are polynomials and $$q(x) 
eq 0$

Question 2

Find the domain of the function $$f(x) = \frac{2x+1}{x^2$-4}.$$

Accepted Answer

$$x 
eq 2, x 
eq -2$$

Question 3

Which of the following describes the vertical asymptote(s) of $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$x = 3$$

Question 4

What is the horizontal asymptote of $$f(x) = \frac{2x^2$+1}{x^2$-5}$$?

Accepted Answer

$$y = 2$$

Question 5

Given $$f(x) = \frac{x^2$-1}{x+1}$$, what is the equation of any hole in the graph?

Accepted Answer

$$x = -1$$

Question 6

Which transformation occurs to the graph of $$f(x) = \frac{1}{x} to $$obtain $$g(x) = \frac{1}{x-2} + 3$$?

Accepted Answer

Shift right 2 units and up 3 units

Question 7

For $$f(x) = \frac{3x}{x^2$-9}$$, which of the following statements is true?

Accepted Answer

There are vertical asymptotes at $$x = 3$$ and $$x = -3$$

Question 8

What is the solution set for the inequality $$x^2 - 4x$$ \leq 0$$?

Accepted Answer

$$0 \leq x \leq 4$$

Question 9

Which of the following best describes the end behavior of $$f(x) = \frac{2x^2$+1}{x^2$-5} as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o 2$$

Question 10

Solve and graph the solution set for $$\frac{x}{x-2} \geq 1.$$

Accepted Answer

$$x \u003c 2 or$$ $$x \geq 3$$

Question 11

Which of the following is the correct process to find the vertical asymptotes of a rational function $$f(x) = \frac{p(x)}{q(x)}$$?

Accepted Answer

Set $$q(x) = 0$$ and solve for $$x$$

Question 12

Given $$f(x) = \frac{2x+3}{x-1}$$, what is the $$y-$$intercept of the function?

Accepted Answer

$$(0, -3)$$

Question 13

If $$f(x) = \frac{x^2$-9}{x-3}$$, what is the simplified form of $$f(x)$$ for $$x 
eq 3$$?

Accepted Answer

$$f(x) = x + 3$$

Question 14

Which of the following describes the slant (oblique) asymptote of $$f(x) = \frac{x^2$+2x+1}{x+1}$$?

Accepted Answer

$$y = x + 1$$

Question 15

Solve the inequality $$\frac{x+2}{x-1} \u003c 0.$$

Accepted Answer

$$-2 \u003c x \u003c 1$$

Question 16

Which of the following is a real-world application of rational functions?

Accepted Answer

Modeling the speed of a chemical reaction as a function of concentration

Question 17

Given $$f(x) = \frac{1}{x^2$}$$, what is the behavior of $$f(x) as$$ $$x$$ approaches 0 from the right?

Accepted Answer

$$f(x) 	o \infty$$

Question 18

Which of the following is the correct solution set for $$x^2 - 5x + 6$$ \u003e 0$$?

Accepted Answer

$$x  3$$

Question 19

For the rational function $$f(x) = \frac{x^2$-4}{x^2$-1}$$, which of the following statements is true?

Accepted Answer

There are vertical asymptotes at $$x = 1$$ and $$x = -1$$

Rational Functions, Their Graphs, and Polynomial & Rational Inequalities

Study Guide - Practice Questions