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.

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'.

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.

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.

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.

Front

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

Back

x = -2

Front

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

Back

y = 2/3

Front

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

Back

x = 2 and x = -2

Front

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

Back

y = 5/2

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.