Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What are the x-intercepts of a function?

Back

The x-intercepts of a function are the points where the graph of the function crosses the x-axis, meaning the output (y-value) is zero.

Front

How do you find the x-intercepts of a rational function?

Back

To find the x-intercepts, set the numerator of the rational function equal to zero and solve for x.

Front

What are asymptotes in rational functions?

Back

Asymptotes are lines that the graph of a function approaches but never touches. They can be vertical, horizontal, or oblique.

Front

What is a vertical asymptote?

Back

A vertical asymptote occurs at values of x that make the denominator of a rational function zero, leading to undefined values.

Front

What is a horizontal asymptote?

Back

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

Front

How do you determine horizontal asymptotes for rational functions?

Back

To find horizontal asymptotes, compare the degrees of the numerator and denominator polynomials.

Front

What is the horizontal asymptote if the degree of the numerator is less than the degree of the denominator?

Back

The horizontal asymptote is y = 0.

Front

What is the horizontal asymptote if the degree of the numerator is equal to the degree of the denominator?

Back

The horizontal asymptote is y = the ratio of the leading coefficients of the numerator and denominator.

Front

What is the horizontal asymptote if the degree of the numerator is greater than the degree of the denominator?

Back

There is no horizontal asymptote; the function may have an oblique asymptote instead.