Graphs of Rational Functions

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a rational 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

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 the graph of a function approaches as x approaches infinity or negative infinity.

Front

When does a horizontal asymptote equal zero?

Back

A horizontal asymptote equals zero when the degree of the numerator is less than the degree of the denominator.

Front

What is a hole in a graph of a rational function?

Back

A hole occurs at a point where both the numerator and denominator of a rational function are zero, indicating that the function is undefined at that point.

Front

How do you identify a hole in a rational function?

Back

To identify a hole, factor both the numerator and denominator, and find common factors that cancel out.

Front

What is the significance of the degrees of the numerator and denominator?

Back

The degrees of the numerator and denominator determine the behavior of the function at infinity and the existence of horizontal asymptotes.

Front

What happens when the degree of the numerator is greater than the degree of the denominator?

Back

When the degree of the numerator is greater than the degree of the denominator, the horizontal asymptote is at y = infinity or negative infinity.

Front

What is the general form of a rational function?

Back

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

Front

How do you determine the x-intercepts of a rational function?

Back

The x-intercepts are found by setting the numerator equal to zero and solving for x.