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 x approaches a. It occurs when the denominator of a rational function equals zero.

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

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 vertical asymptotes in rational functions?

Back

Vertical asymptotes are found by setting the denominator of a rational function equal to zero and solving for x.

Front

How do you determine horizontal asymptotes for rational functions?

Back

Horizontal asymptotes can be determined by comparing the degrees of the numerator and denominator. If the degree of the numerator is less than the denominator, y = 0; if they are equal, y = the ratio of leading coefficients; if the numerator's degree is greater, there is no horizontal asymptote.

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 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 constant value.

Front

What is the significance of the denominator in determining asymptotes?

Back

The denominator of a rational function is crucial for determining vertical asymptotes, as it indicates where the function is undefined.

Front

What is the end behavior of a function?

Back

The end behavior of a function describes how the function behaves as x approaches positive or negative infinity, often analyzed through horizontal asymptotes.

Front

What is the relationship between zeros and x-intercepts?

Back

Zeros of a function correspond to the x-intercepts of its graph, where the function crosses the x-axis.