Graphing Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

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 a removable discontinuity.

Front

How do you find the coordinates of a hole in a rational function?

Back

To find the coordinates of a hole, factor the numerator and denominator, cancel the common factors, and substitute the x-value of the canceled factor into the simplified function.

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 a non-removable discontinuity.

Front

How do you find vertical asymptotes in a rational function?

Back

Set the denominator equal to zero and solve for x to find the vertical asymptotes.

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.

Front

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

Back

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 domain of a rational function?

Back

The domain of a rational function includes all real numbers except for the values that make the denominator zero.

Front

How do you find the domain of a rational function?

Back

Identify the values of x that make the denominator zero and exclude them from the set of all real numbers.