Attributes/Transformations Test

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as the input approaches a. It indicates where the function is undefined.

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 the graph of a function approaches as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine horizontal asymptotes for rational functions?

Back

For rational functions, 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, no horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What does it mean if a function has a vertical asymptote at x = 3?

Back

It means that as x approaches 3, the function's value increases or decreases without bound, indicating a point of discontinuity.

Tags

CCSS.HSF-IF.C.7D

Front

What does it mean if a function has a horizontal asymptote at y = -5?

Back

It means that as x approaches infinity or negative infinity, the function's value approaches -5, indicating the function levels off.

Tags

CCSS.HSF-IF.C.7D

Front

Can a function have both vertical and horizontal asymptotes?

Back

Yes, a function can have both vertical and horizontal asymptotes, indicating different behaviors as x approaches certain values and as x goes to infinity.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of asymptotes in graphing functions?

Back

Asymptotes help identify the behavior of a function near points of discontinuity and at extreme values, guiding the overall shape of the graph.

Tags

CCSS.HSF-IF.C.7D

Front

What is the relationship between asymptotes and limits?

Back

Asymptotes are closely related to limits; vertical asymptotes occur where the limit of the function approaches infinity, while horizontal asymptotes relate to the limit of the function as x approaches infinity.

Tags

CCSS.HSF-IF.C.7D

Front

What is an example of a function with a vertical asymptote?

Back

The function f(x) = 1/(x-3) has a vertical asymptote at x = 3.

Tags

CCSS.HSF-IF.C.7D