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?

Back

Vertical asymptotes are 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 the graph of a rational function approaches as x approaches infinity or negative infinity.

Front

How do you find horizontal asymptotes?

Back

Horizontal asymptotes can be found by comparing the degrees of the numerator and denominator polynomials.

Front

What is a hole in a graph of a rational function?

Back

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

Front

How do you identify holes in a rational function?

Back

To identify holes, factor both the numerator and denominator and find common factors that can be canceled.

Front

What is the significance of the degree of the numerator and denominator?

Back

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

Front

What is a slant asymptote?

Back

A slant asymptote occurs when the degree of the numerator is one greater than the degree of the denominator.

Front

How do you find slant asymptotes?

Back

Slant asymptotes can be found using polynomial long division of the numerator by the denominator.