Graphing Rational Functions Practice

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 of a rational function, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If they are equal, the asymptote is y = (leading coefficient of numerator)/(leading coefficient of denominator). If the degree of the numerator is greater, there is no horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What is the domain of a rational function?

Back

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

Front

What is the range of a rational function?

Back

The range of a rational function is all real numbers except for the value of the horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What are vertical asymptotes?

Back

Vertical asymptotes are vertical lines that the graph of a function approaches as x approaches a certain value, typically where the denominator of a rational function is zero.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of asymptotes in graphing rational functions?

Back

Asymptotes help to determine the behavior of the graph of a rational function, indicating where the graph will not cross or touch certain lines.

Tags

CCSS.HSF-IF.C.7D

Front

What is the difference between a hole and a vertical asymptote?

Back

A hole occurs when a factor in the numerator and denominator cancels out, indicating a point where the function is undefined. A vertical asymptote occurs where the function approaches infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine the intercepts of a rational function?

Back

To find the x-intercepts, set the numerator equal to zero and solve for x. To find the y-intercept, evaluate the function at x = 0.

Tags

CCSS.HSF-IF.C.7D

Front

What is the end behavior of a rational function?

Back

The end behavior of a rational function describes how the function behaves as x approaches positive or negative infinity, often determined by the horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D