Rational Functions

Front

What is a rational function?

Back

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity. It indicates the behavior of the function at extreme values.

Front

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

Back

To find the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator: If the degree of the numerator is less than the degree of the denominator, the asymptote is y=0. If they are equal, the asymptote is y=\frac{a}{b}, where a and b are the leading coefficients.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = k where the function approaches infinity or negative infinity. It occurs at values of x that make the denominator of a rational function equal to zero.

Front

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

Back

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

Front

What are x-intercepts?

Back

X-intercepts are points where the graph of a function crosses the x-axis. For rational functions, they occur where the numerator is equal to zero.

Front

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

Back

To find the x-intercepts, 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 is the set of all real numbers except for the values that make the denominator equal to zero.

Front

What is a hole in a rational function?

Back

A hole occurs in the graph of a rational function at a value of x that makes both the numerator and denominator equal to zero. It represents a point that is not included in the domain.

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. The x-value of the common factor is where the hole occurs.