Graphing 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.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the domain of a rational function?

Back

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

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a.

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine vertical asymptotes from a rational function?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that the function approaches as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes for rational functions?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

What happens to a rational function at its vertical asymptotes?

Back

At vertical asymptotes, the function's value approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of the numerator in a rational function?

Back

The numerator determines the function's zeros, which are the x-values where the function equals zero.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of the denominator in a rational function?

Back

The denominator determines the function's vertical asymptotes and the domain restrictions.

Tags

CCSS.HSF-IF.C.7D

Front

How do you simplify a rational function?

Back

To simplify a rational function, factor both the numerator and denominator and cancel out any common factors.

Tags

CCSS.HSA.APR.D.6