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 vertical asymptotes?

Back

Vertical asymptotes are lines x = a where a rational function approaches infinity or negative infinity as x approaches a.

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes can be found by setting the denominator of the rational function equal to zero and solving for x.

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes are lines y = b that a rational function approaches as x approaches infinity or negative infinity.

Front

How do you determine horizontal asymptotes of a rational function?

Back

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

Front

What is an x-intercept?

Back

An x-intercept is a point where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Front

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

Back

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

Front

What is a hole in a rational function?

Back

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

Front

How do you find the coordinates of a hole in a rational function?

Back

To find the hole, factor the numerator and denominator, cancel the common factors, and evaluate the function at the x-value of the canceled factor.

Front

What is the significance of the degree of the numerator and denominator in rational functions?

Back

The degree of the numerator and denominator helps determine the behavior of the function, including the existence of horizontal asymptotes.