Vertical and Horizontal Asymptotes

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.

Front

How do you find vertical asymptotes in a rational function?

Back

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

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.

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.

Front

What does it mean if a function has no vertical asymptotes?

Back

If a function has no vertical asymptotes, it means the denominator does not equal zero for any real number x.

Front

What is the significance of the dotted green line in a graph?

Back

The dotted green line typically represents a vertical asymptote in a 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 happens to the function value as it approaches a vertical asymptote?

Back

As the function approaches a vertical asymptote, the function value tends to either positive or negative infinity.

Front

What is the general form of a rational function?

Back

A rational function is generally expressed as f(x) = P(x)/Q(x), where P and Q are polynomials.

Front

How can you identify the vertical asymptotes from the function g(x) = (2x^2 + x - 9)/(x^2 - 2x - 8)?

Back

Set the denominator x^2 - 2x - 8 equal to zero and solve for x to find vertical asymptotes.