Rational Functions

Front

What is a rational function?

Back

Front

What is a vertical asymptote?

Back

Front

How do you find vertical asymptotes of a rational function?

Back

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

Front

What is a horizontal asymptote?

Back

Front

How do you determine horizontal asymptotes for rational functions?

Back

Front

What is the significance of the leading coefficient in rational functions?

Back

The leading coefficient of the numerator and denominator helps determine the end behavior of the function and the horizontal asymptote.

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except for the values that make the denominator zero.

Front

What is the range of a rational function?

Back

The range of a rational function can vary widely, but it often excludes the y-values corresponding to horizontal asymptotes.

Front

What does it mean for a rational function to have no horizontal asymptote?

Back

A rational function has no horizontal asymptote if the degree of the numerator is greater than the degree of the denominator.

Front

How do you graph a rational function?

Back

To graph a rational function, identify vertical and horizontal asymptotes, intercepts, and test points in the intervals defined by the asymptotes.