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

What are horizontal asymptotes?

Back

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

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

How do you find horizontal asymptotes?

Back

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

Front

What is the domain of a rational function?

Back

The domain of a rational function includes all real numbers except where the denominator equals zero.

Front

What happens to the graph of a rational function at vertical asymptotes?

Back

The graph of a rational function will approach the vertical asymptote but will never touch or cross it.

Front

What is a slant (oblique) asymptote?

Back

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

Front

When does a rational function 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

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 rational function at infinity and the existence of asymptotes.