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.

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.

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.

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.

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.

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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.

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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.

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.

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.

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.