Graphing Rational Functions

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line that a graph approaches but never touches or crosses. It occurs where the function is undefined.

Front

What does it mean when a function has a vertical asymptote at x = 6?

Back

It means that as the value of x approaches 6, the value of the function increases or decreases without bound.

Front

What is an asymptote?

Back

An asymptote is an imaginary line that a graph approaches as it heads towards infinity.

Front

What are the horizontal asymptotes of a rational function?

Back

Horizontal asymptotes indicate the behavior of a function as x approaches infinity or negative infinity.

Front

How do you find vertical asymptotes in a rational function?

Back

Set the denominator of the rational function equal to zero and solve for x.

Front

Back

The horizontal asymptote is y = 2, as the degree of the numerator and denominator are the same.

Front

What is the significance of the x-intercept in a rational function?

Back

The x-intercept is the point where the graph crosses the x-axis, found by setting the numerator equal to zero.

Front

Back

The y-intercept is found by evaluating the function at x = 0, which gives y = -0.5.

Front

What happens to the graph of a rational function at its vertical asymptotes?

Back

The graph will approach the vertical asymptote but will never touch or cross it.

Front

How do you determine the end behavior of a rational function?

Back

Analyze the degrees of the numerator and denominator to find the horizontal asymptote.