Asymptotes in Rational Functions Review

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It occurs when the denominator of a rational function equals zero and the numerator does not.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes in a rational function?

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 a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity. It indicates the behavior of the function at extreme values.

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine horizontal asymptotes in rational functions?

Back

To determine horizontal asymptotes, compare the degrees of the numerator and denominator. If the degree of the numerator is less, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, there is no horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What is a hole in a rational function?

Back

A hole occurs in a rational function at a point where both the numerator and denominator are zero, indicating that the function is undefined at that point but can be simplified.

Tags

CCSS.HSF-IF.C.7D

Front

How do you identify holes in a rational function?

Back

To identify holes, factor both the numerator and denominator, and find common factors. The x-values of these common factors indicate the location of the holes.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of vertical asymptotes?

Back

Vertical asymptotes indicate values of x where the function is undefined and help in understanding the behavior of the graph near those points.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of horizontal asymptotes?

Back

Horizontal asymptotes indicate the end behavior of a function as x approaches infinity or negative infinity, helping to predict the function's long-term behavior.

Tags

CCSS.HSF-IF.C.7D

Front

Back

There is a hole at x = 1 because both the numerator and denominator equal zero at this point.

Tags

CCSS.HSF-IF.C.7D

Front

Back

The vertical asymptotes are at x = 2 and x = 3, found by setting the denominator equal to zero.

Tags

CCSS.HSF-IF.C.7D