Asymptotes

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

How do you determine the horizontal asymptote of a rational function?

Back

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

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the input approaches a certain value, typically where the function is undefined.

Front

How do you find vertical asymptotes in a rational function?

Back

Vertical asymptotes occur at values of x that make the denominator zero, provided those values do not also make the numerator zero.

Front

What is a hole in a rational function?

Back

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

Front

What happens to the horizontal asymptote when the degree of the numerator is less than the degree of the denominator?

Back

The horizontal asymptote is y=0.

Front

What happens to the horizontal asymptote when the degree of the numerator is greater than the degree of the denominator?

Back

There is no horizontal asymptote.

Front

If a rational function has a degree of 2 in the numerator and degree of 1 in the denominator, what is the horizontal asymptote?

Back

There is no horizontal asymptote.

Front

What is the significance of the leading coefficients in determining horizontal asymptotes?

Back

The leading coefficients of the numerator and denominator determine the value of the horizontal asymptote when the degrees are equal.