Horizontal and Vertical Asymptotes

Front

What are asymptotes?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical, horizontal, or oblique.

Tags

CCSS.HSF-IF.C.7D

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = a where the function approaches infinity or negative infinity as x approaches a.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes are found by setting the denominator of a rational function to zero and solving for x.

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes for rational functions?

Back

1. If the degree of the numerator is less than the degree of the denominator, y = 0. 2. If they are equal, y = leading coefficient of numerator / leading coefficient of denominator. 3. If the numerator's degree is greater, there is no horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What are the vertical asymptotes of the function f(x) = 1/(x^2 - 4)?

Back

x = 2 and x = -2.

Tags

CCSS.HSF-IF.C.7D

Front

What is the horizontal asymptote of the function f(x) = 3x^2 + 2 / 4x^2 + 5?

Back

y = 3/4.

Tags

CCSS.HSF-IF.C.7D

Front

True or False: To find the horizontal asymptote, you use the numerator.

Back

False.

Tags

CCSS.HSF-IF.C.7D

Front

What happens to the graph of a function as it approaches a vertical asymptote?

Back

The graph will increase or decrease without bound (approach infinity or negative infinity).

Tags

CCSS.HSF-IF.C.7D

Front

Can a function cross its horizontal asymptote?

Back

Yes, a function can cross its horizontal asymptote, especially in the case of rational functions.

Tags

CCSS.HSF-IF.C.7D