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

What is the general form of a rational function?

Back

The general form of a rational function is f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

What is an asymptote in the context of rational functions?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

The horizontal asymptote can be determined by comparing the degrees of the numerator and denominator polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

What happens to the horizontal asymptote when 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 to the horizontal asymptote when 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 of the numerator and denominator.

Tags

CCSS.HSF-IF.C.7D

Front

What happens to the horizontal asymptote when the degree of the numerator is greater than the degree of the denominator?

Back

There is no horizontal asymptote; the function may have an oblique asymptote instead.

Tags

CCSS.HSF-IF.C.7D

Front

What is a hole in a rational function?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

What are x-intercepts in a rational function?

Back

X-intercepts are the points where the graph of the function crosses the x-axis, found by setting the numerator equal to zero.

Tags

CCSS.HSF-IF.C.7D