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 and the numerator does not.

Front

How do you find the vertical asymptote of a rational function?

Back

To find the vertical asymptote, set the denominator of the rational function equal to zero and solve for x.

Front

What is a hole in a rational function?

Back

A hole occurs in a rational function at a point where both the numerator and denominator are zero, indicating that the function is undefined at that point but can be simplified.

Front

How do you find the holes in a rational function?

Back

To find holes, factor both the numerator and denominator, identify common factors, and set them equal to zero.

Front

What are domain restrictions in rational functions?

Back

Domain restrictions are values of x that make the denominator zero, which are not included in the domain of the function.

Front

How do you determine the domain of a rational function?

Back

To determine the domain, find the values of x that make the denominator zero and exclude them from the set of all real numbers.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line y = b that the graph of a function approaches as x approaches infinity or negative infinity.

Front

How do you find horizontal asymptotes for rational functions?

Back

To find horizontal asymptotes, 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 is the significance of the y-intercept in a rational function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.

Front

How do you find the y-intercept of a rational function?

Back

To find the y-intercept, substitute x = 0 into the function and solve for f(0).