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

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the horizontal asymptote of a rational function?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

What happens if the degree of the numerator is less than the degree of the denominator?

Back

The horizontal asymptote is y = 0.

Tags

CCSS.HSF-IF.C.7D

Front

What happens 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.

Tags

CCSS.HSF-IF.C.7D

Front

What happens if the degree of the numerator is greater than the degree of the denominator?

Back

There is no horizontal asymptote; the function may have a slant asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the function's value approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes in a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator equal to zero, provided those values do not also make the numerator zero.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of the x-intercept in a rational function?

Back

The x-intercept is the point where the graph crosses the x-axis, found by setting the numerator equal to zero.

Tags

CCSS.HSF-IF.C.7D