Unit 5 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 indicates values that the function cannot take.

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes occur at values of x that make the denominator zero, provided the numerator is not also zero at those points.

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 end behavior of the function.

Front

How do you determine horizontal asymptotes for rational functions?

Back

1. If the degree of the numerator is less than the degree of the denominator, y = 0 is the horizontal asymptote. 2. If the degrees are equal, y = leading coefficient of numerator / leading coefficient of denominator. 3. If the degree of the numerator is greater, there is no horizontal asymptote.

Front

What is a zero of a function?

Back

A zero of a function is a value of x for which the function f(x) = 0. It represents the x-intercepts of the graph.

Front

How do you find the x-intercepts of a function?

Back

To find the x-intercepts, set the function equal to zero and solve for x.

Front

What is a slant (oblique) asymptote?

Back

A slant asymptote occurs when the degree of the numerator is exactly one more than the degree of the denominator. It can be found using polynomial long division.

Front

What is the significance of asymptotes in graphing functions?

Back

Asymptotes help identify the behavior of a function as it approaches certain values, guiding the sketching of the graph and understanding limits.

Front

What does it mean if a function has no horizontal asymptote?

Back

If a function has no horizontal asymptote, it means that as x approaches infinity or negative infinity, the function does not approach a finite value.

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, as the function is undefined at those points.