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.

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.

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.

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.

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.

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) = 3x^2 + 2 / 4x^2 + 5?

Back

y = 3/4.

Front

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

Back

False.

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).

Front

Can a function cross its horizontal asymptote?

Back

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