Asymptotes

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or intersects. It 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 the input approaches 'a'.

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 of a function approaches as the input approaches positive or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes for rational functions?

Back

For rational functions, compare the degrees of the numerator and denominator: If the degree of the numerator is less, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, there is no horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What is the vertical asymptote of the function f(x) = 1/(x + 2)?

Back

x = -2

Tags

CCSS.HSF-IF.C.7D

Front

What is the horizontal asymptote of the function f(x) = 2x/(3x + 1)?

Back

y = 2/3

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) = 5x^2/(2x^2 + 3)?

Back

y = 5/2

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

The graph will approach infinity or negative infinity as it gets close to the vertical asymptote.

Tags

CCSS.HSF-IF.C.7D