Graphing Rational Functions

Front

What are x-intercepts?

Back

The x-intercepts of a function are the points where the graph intersects the x-axis. For rational functions, they occur when the numerator is zero.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

A hole occurs at the x-value where a factor in both the numerator and denominator cancels out. To find the coordinates, substitute this x-value into the simplified function.

Tags

CCSS.HSF-IF.C.7D

Front

What is the domain of a rational function?

Back

The domain of a rational function includes all real numbers except for values that make the denominator zero.

Front

What is end behavior in graphing?

Back

End behavior describes how the values of a function behave as x approaches positive or negative infinity.

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

To find the horizontal asymptote, compare the degrees of the numerator and denominator. If they are equal, divide the leading coefficients.

Tags

CCSS.HSF-IF.C.7D

Front

What does it mean if a rational function has a hole?

Back

A hole indicates that there is a removable discontinuity in the function, often due to a common factor in the numerator and denominator.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of vertical asymptotes?

Back

Vertical asymptotes indicate values of x where the function approaches infinity or negative infinity, typically where the denominator is zero.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes?

Back

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

Tags

CCSS.HSF-IF.C.7D

Front

What is the relationship between the degree of the numerator and the degree of the denominator?

Back

The degree of the numerator and denominator helps determine the end behavior and horizontal asymptotes of the rational function.

Tags

CCSS.HSF-IF.C.7D