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 values that the function cannot take.

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 the input approaches 3, the output of the function increases or decreases without bound.

Front

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

Back

It means that as the input values become very large or very small, the output of the function approaches -5.

Front

Can a function cross its horizontal asymptote?

Back

Yes, a function can cross its horizontal asymptote; the asymptote describes the behavior of the function as x approaches infinity or negative infinity, not at finite values.

Front

What is the significance of asymptotes in graphing functions?

Back

Asymptotes help identify the behavior of a function at extreme values and guide the overall shape of the graph.

Front

What is the relationship between vertical asymptotes and the domain of a function?

Back

Vertical asymptotes indicate values that are excluded from the domain of the function.

Front

What is the difference between a removable and non-removable discontinuity?

Back

A removable discontinuity occurs when a factor cancels in a rational function, while a non-removable discontinuity occurs at vertical asymptotes where the function is undefined.