Content Check Rational Functions

Front

What are asymptotes in rational functions?

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 occurs where the denominator of a rational function is zero, indicating a point of discontinuity.

Front

How do you find vertical asymptotes?

Back

Set the denominator of the rational function equal to zero and solve for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote indicates the behavior of a function as x approaches infinity or negative infinity.

Front

How do you determine horizontal asymptotes?

Back

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, no horizontal asymptote.

Front

What is an oblique (slant) asymptote?

Back

An oblique asymptote occurs when the degree of the numerator is one more than the degree of the denominator.

Front

How do you find an oblique asymptote?

Back

Perform polynomial long division on the rational function.

Front

What does it mean for a function to be discontinuous?

Back

A function is discontinuous at a point where it is not defined or does not have a limit.

Front

How can you identify points of discontinuity in rational functions?

Back

Look for values of x that make the denominator zero.

Front

What is the significance of the x-intercept in a rational function?

Back

The x-intercept is the point where the graph crosses the x-axis, found by setting the numerator equal to zero.