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 are the key features to identify when graphing a rational function?

Back

Key features include intercepts, asymptotes (vertical and horizontal), and the behavior of the function as it approaches these asymptotes.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the vertical asymptotes of a rational function?

Back

Vertical asymptotes occur where the denominator of the rational function is equal to zero, provided the numerator is not also zero at those points.

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 determine the horizontal asymptote of a rational function?

Back

The horizontal asymptote can be determined by comparing the degrees of the numerator and denominator: if the degree of the numerator is less, the asymptote is y=0; if they are equal, y is the ratio of leading coefficients; if the numerator's degree is greater, there is no horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of intercepts in graphing rational functions?

Back

Intercepts (x-intercepts and y-intercepts) indicate where the graph crosses the axes, providing key points for sketching the graph.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the x-intercepts of a rational function?

Back

X-intercepts are found by setting the numerator of the rational function equal to zero and solving for x.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the y-intercept of a rational function?

Back

The y-intercept is found by evaluating the function at x=0, provided the function is defined at that point.

Tags

CCSS.HSF-IF.C.7D

Front

What is the behavior of a rational function near its vertical asymptotes?

Back

As the function approaches a vertical asymptote, the function values will tend to positive or negative infinity, depending on the direction of approach.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

A hole occurs at a point where both the numerator and denominator are zero, indicating that the function is not defined at that point, but the graph approaches it.

Tags

CCSS.HSF-IF.C.7D