Steps for Graphing Rational Functions

Front

What are holes in a rational function?

Back

Holes occur at values of x where factors in the numerator and denominator cancel out.

Front

How do you find holes in a rational function?

Back

Identify factors that cancel in the function.

Front

What are vertical asymptotes in a rational function?

Back

Vertical asymptotes are lines that the graph approaches but never touches, occurring where the denominator is zero.

Front

How do you find vertical asymptotes in a rational function?

Back

Set the denominator equal to zero and solve for x.

Front

What are x-intercepts in a rational function?

Back

X-intercepts are points where the graph crosses the x-axis, occurring when the numerator is zero.

Front

How do you find x-intercepts in a rational function?

Back

Set the numerator equal to zero and solve for x.

Front

What is the first step in graphing rational functions?

Back

The first step is to factor the rational function.

Front

What is the end behavior of a rational function?

Back

End behavior describes how the function behaves as x approaches positive or negative infinity.

Front

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

Back

The degree helps determine the end behavior and the number of asymptotes.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph approaches as x approaches infinity.