How do you find the y-intercept of the function $$f(x) = -\frac{4}{x-3}$$ ?

To find the y-intercept, substitute $$x = 0$$ into the function: $$f(0) = -\frac{4}{0-3} = \frac{4}{3}$$ .

Given the function $$f(x) = \frac{1}{x-2}$$ , what is the vertical asymptote?

The vertical asymptote is at $$x = 2$$ .

What is the x-intercept of a function?

The x-intercept of a function is the point where the graph intersects the x-axis, which occurs when $$f(x) = 0$$ .

How do you find the x-intercept of the function $$f(x) = -\frac{4}{x-3}$$ ?

Set the function equal to zero: $$-\frac{4}{x-3} = 0$$ . This gives no solution, indicating there is no x-intercept.

What is the significance of the degree of the numerator and denominator in a rational function?

The degree of the numerator and denominator helps determine the end behavior of the function and the presence of horizontal asymptotes.

What is a horizontal asymptote?

A horizontal asymptote is a horizontal line $$y = b$$ that the graph of a function approaches as $$x$$ approaches infinity or negative infinity.

How do you find horizontal asymptotes for rational functions?

Compare the degrees of the numerator and denominator: If the degree of the numerator is less, the horizontal asymptote is $$y = 0$$ ; if equal, $$y = \frac{a}{b}$$ where a and b are leading coefficients.

What happens to the graph of a rational function at a vertical asymptote?

As the function approaches the vertical asymptote, the graph will rise or fall towards infinity or negative infinity.

What is the relationship between holes and vertical asymptotes?

Holes indicate removable discontinuities, while vertical asymptotes indicate non-removable discontinuities in the graph of a rational function.

Given the function $$f(x) = \frac{1}{x^2 - 4}$$ , identify the vertical asymptotes.

The vertical asymptotes are at $$x = 2$$ and $$x = -2$$ , where the denominator equals zero.

Rational Function Graphs

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

Wayground Content

FREE Resource

Student preview

15 questions

Show all answers

FLASHCARD QUESTION

Front

What is a rational function?

Back

FLASHCARD QUESTION

Front

What is the y-intercept of a function?

Back

FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

What is a vertical asymptote?

Back

FLASHCARD QUESTION

Front

How do you determine vertical asymptotes of a rational function?

Back

FLASHCARD QUESTION

Front

What is a hole in a graph of a rational function?

Back

A hole occurs in the graph of a rational function at a point where both the numerator and denominator are zero, indicating a removable discontinuity.

FLASHCARD QUESTION

Front

Back

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

10 questions

Mandarin Fruits

Flashcard

•

15 questions

paměť + pozornost

Flashcard

•

9th - 12th Grade

7 questions

International Yoga Day Quiz

Flashcard

•

KG - University

16 questions

April Fools Trivia

Flashcard

•

KG - University

10 questions

Present Simple - Negative

Flashcard

•

10th Grade

4 questions

5.2. Asymptotes Verticales

Flashcard

•

9th - 12th Grade

12 questions

Political Advocacy and Interest Groups

Flashcard

•

9th - 12th Grade

Popular Resources on Wayground

10 questions

5.P.1.3 Distance/Time Graphs

Quiz

•

5th Grade

10 questions

Fire Drill

Quiz

•

2nd - 5th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

15 questions

Hargrett House Quiz: Community & Service

Quiz

•

5th Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

20 questions

Inferences

Quiz

•

4th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

Discover more resources for Mathematics

20 questions

Graphing Inequalities on a Number Line

Quiz

•

6th - 9th Grade

10 questions

Exploring Basic Probability Concepts

Interactive video

•

6th - 10th Grade

11 questions

Adding and Subtracting Polynomials

Quiz

•

9th Grade

20 questions

Rational and Irrational Numbers, Perfect Squares, & Perfect Cube

Quiz

•

9th Grade

12 questions

Exponential Growth and Decay

Quiz

•

9th Grade

10 questions

Factoring Quadratic Expressions

Quiz

•

9th Grade

16 questions

Identifying Angles

Quiz

•

7th - 12th Grade

25 questions

Complementary and Supplementary Angles

Quiz

•

7th - 10th Grade