Which statement describes the domain of the function f(x)=3x/$$4x^2$$-4?

all real numbers except x=-1 and x=1

all real numbers except x=-2 and x=1

all real numbers except x=1 and x=2

all real numbers except x=-1 and x=2

Which statement describes the behavior of the function f(x)=2x/1-$$x^2$$?

The graph approaches 0 as x approaches infinity.

The graph approaches 1 as x approaches infinity.

The graph approaches -1 as x approaches infinity.

The graph approaches 2 as x approaches infinity.

What is an asymptote?

an imaginary line that your function never touches

an imaginary line that your function always touches

Graphing Rational Functions Quiz

Created by ProProfs Editorial Team

The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.

Learn about Our Editorial Process

| By Sophia Smith

Sophia Smith, Quiz Creator

Sophia is a skilled quiz creator at ProProfs.com, known for her engaging and innovative quizzes. Her enthusiasm for learning and creativity results in quizzes that are both fun and educational. Sophia's dedication to excellence ensures that users always have a top-notch experience with her interactive content.

Quizzes Created: 1083 | Total Attempts: 3,181,141

Questions: 10 | Attempts: 156 | Updated: Aug 16, 2023

Questions

Settings

Feedback

During the Quiz End of Quiz

Difficulty

Sequential Easy First Hard First

Play as

Quiz Flashcard

Create your own Quiz

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

Do you know rational functions? Do you know how to put them in the graph? Take this graphing rational functions quiz to check your knowledge and understanding of this module. Here, we have a few basic questions that will help you know the level of your knowledge about graphing of rational functions. Give this quiz a try, and see how much you score. All the best! You can also share your score with other math lovers and help them practice this module.

Questions and Answers

1.

Which statement describes the domain of the function f(x)=3x/4x^2-4?
- A.
  
  All real numbers except x=-2 and x=1
- B.
  
  All real numbers except x=-1 and x=1
- C.
  
  All real numbers except x=1 and x=2
- D.
  
  All real numbers except x=-1 and x=2
Correct Answer
B. All real numbers except x=-1 and x=1

Explanation
The given function is a rational function. In a rational function, the denominator cannot be equal to zero. Therefore, the domain of the function is all real numbers except for the values of x that make the denominator zero. In this case, the denominator is 4x^2-4, which can be factored as 4(x^2-1). Setting this equal to zero, we get x^2-1=0, which factors as (x-1)(x+1)=0. So, the values of x that make the denominator zero are x=-1 and x=1. Therefore, the domain of the function is all real numbers except x=-1 and x=1.

Rate this question:
2.

What is the horizontal asymptote of f(x)=-2x/x+1?
- A.
  
  Y= -2
- B.
  
  Y= 1
- C.
  
  Y= -1
- D.
  
  Y= 2
Correct Answer
A. Y= -2

Explanation
The horizontal asymptote of a function represents the value that the function approaches as x approaches positive or negative infinity. In this case, as x becomes very large or very small, the term -2x in the numerator will dominate the term x+1 in the denominator. Therefore, the function will approach -2 as x approaches infinity or negative infinity, making y = -2 the horizontal asymptote.

Rate this question:
3.

Which statement describes the behavior of the function f(x)=2x/1-x^2?
- A.
  
  The graph approaches 1 as x approaches infinity.
- B.
  
  The graph approaches -1 as x approaches infinity.
- C.
  
  The graph approaches 2 as x approaches infinity.
- D.
  
  The graph approaches 0 as x approaches infinity.
Correct Answer
D. The grapH approaches 0 as x approaches infinity.

Explanation
As x approaches infinity, the denominator x^2 becomes extremely large compared to the numerator 2x. Therefore, the fraction 2x/1-x^2 approaches 0. This can be seen by considering the limit of the function as x approaches infinity, where the numerator remains finite while the denominator grows without bound.

Rate this question:
4.

What is the Y-intercept of y=(x+5)/(x-6)?
- A.
  
  (0, 5)
- B.
  
  (0, -5/6)
- C.
  
  (0, 1)
- D.
  
  (0, -6)
Correct Answer
B. (0, -5/6)

Explanation
The y-intercept of a function is the point where the graph of the function intersects the y-axis. To find the y-intercept, we substitute x=0 into the equation and solve for y. In this case, when x=0, the equation becomes y=(0+5)/(0-6) = 5/-6 = -5/6. Therefore, the y-intercept of y=(x+5)/(x-6) is (0, -5/6).

Rate this question:
5.

What is the horizontal asymptote to this function f(x)= (4x+1)/(x+2)?
- A.
  
  Y=4
- B.
  
  Y=2
- C.
  
  Y=0
- D.
  
  Y=1
Correct Answer
A. Y=4

Explanation
The horizontal asymptote of a function represents the value that the function approaches as x approaches positive or negative infinity. In this case, as x becomes very large or very small, the term (4x+1)/(x+2) approaches 4. Therefore, the horizontal asymptote of the function f(x) = (4x+1)/(x+2) is y = 4.

Rate this question:
6.

What is the X-Intercept of y= 4x/(x+5)?
- A.
  
  X=-5
- B.
  
  X=0
- C.
  
  X=4
- D.
  
  X=5
Correct Answer
B. X=0

Explanation
The x-intercept of a function represents the point where the function intersects the x-axis. In this case, to find the x-intercept of the equation y=4x/(x+5), we set y=0 and solve for x. By substituting y=0 into the equation, we get 0=4x/(x+5). Multiplying both sides by (x+5), we eliminate the denominator and obtain 0=4x. Dividing both sides by 4, we find x=0. Therefore, the x=0 is the x-intercept of the given equation.

Rate this question:
7.

What is an asymptote?
- A.
  
  A point on your graph
- B.
  
  A part of your function
- C.
  
  An imaginary line that your function never touches
- D.
  
  An imaginary line that your function always touches
Correct Answer
C. An imaginary line that your function never touches

Explanation
An asymptote is an imaginary line that a function never touches. It is a line that the graph of a function approaches but does not intersect or cross. Asymptotes can be vertical, horizontal, or oblique, and they help to describe the behavior of a function as it approaches infinity or negative infinity. They provide information about the limits of a function and help to understand its overall shape and characteristics.

Rate this question:
8.

Which asymptote(s) are determined by looking at the denominator?
- A.
  
  Slant
- B.
  
  Vertical
- C.
  
  Horizontal
- D.
  
  All of the above
Correct Answer
B. Vertical

Explanation
The asymptotes determined by looking at the denominator are the vertical asymptotes. This is because the vertical asymptotes occur at the values of x where the denominator is equal to zero. When the denominator is zero, the fraction becomes undefined, resulting in a vertical line that the graph approaches but never touches. Therefore, the correct answer is "Vertical."

Rate this question:
9.

What is the domain of y= 1/(x+3)?
- A.
  
  All Reals Except -3
- B.
  
  All Reals Except 0 and -3
- C.
  
  All Reals Except 0
- D.
  
  All Reals
Correct Answer
A. All Reals Except -3

Explanation
The domain of a function is the set of all possible values that the independent variable (x) can take. In this case, the function is y=1/(x+3). The denominator of the fraction cannot be zero, so x+3 cannot be equal to zero. Therefore, the value of x cannot be -3. Hence, the domain of the function is all real numbers except -3.

Rate this question:
10.

What is the Vertical Asymptotes of y= (x+5)/(x-6)?
- A.
  
  X=-6
- B.
  
  X=-5
- C.
  
  X=5
- D.
  
  X=6
Correct Answer
D. X=6

Explanation
The vertical asymptote of a rational function occurs at the values of x that make the denominator equal to zero. In this case, the denominator is x-6, so the vertical asymptote occurs when x-6=0. Solving for x, we find that x=6. Therefore, the vertical asymptote of the given function is x=6.

Rate this question:

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

Current Version
Aug 16, 2023

Quiz Edited by
ProProfs Editorial Team
Nov 01, 2022

Quiz Created by
Sophia Smith

Graphing Rational Functions Quiz

Which statement describes the domain of the function f(x)=3x/4x^2-4?

What is the horizontal asymptote of f(x)=-2x/x+1?

Which statement describes the behavior of the function f(x)=2x/1-x^2?

What is the Y-intercept of y=(x+5)/(x-6)?

What is the horizontal asymptote to this function f(x)= (4x+1)/(x+2)?

What is the X-Intercept of y= 4x/(x+5)?

What is an asymptote?

Which asymptote(s) are determined by looking at the denominator?

What is the domain of y= 1/(x+3)?

What is the Vertical Asymptotes of y= (x+5)/(x-6)?