Graphing Rational Functions

Front

What is a rational function?

Back

Front

What is a hole in a rational function?

Back

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

Front

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

Back

To find the x-intercept, set the numerator of the rational function equal to zero and solve for x.

Front

What is the domain of a rational function?

Back

The domain of a rational function includes all real numbers except where the denominator is zero.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

Front

What is a vertical asymptote?

Back

A vertical asymptote occurs at values of x that make the denominator of a rational function zero, indicating that the function approaches infinity.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote describes the behavior of a function as x approaches infinity or negative infinity, indicating the value that the function approaches.

Front

How do you determine the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator: if they are equal, divide the leading coefficients; if the degree of the numerator is less, the asymptote is y=0; if greater, there is no horizontal asymptote.

Front

What is the significance of the leading coefficient in a rational function?

Back

The leading coefficient affects the end behavior of the graph of the rational function, influencing whether it rises or falls as x approaches infinity.

Front

What is the relationship between holes and asymptotes?

Back

Holes indicate points where the function is undefined due to common factors in the numerator and denominator, while vertical asymptotes indicate values where the function approaches infinity.