HW: Graphing Rational Functions

Front

What are asymptotes?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical, horizontal, or oblique.

Tags

CCSS.HSF-IF.C.7D

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = a where the function approaches infinity or negative infinity as x approaches a.

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line y = b that the graph approaches as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

When does a horizontal asymptote equal zero?

Back

A horizontal asymptote equals zero when the degree of the numerator is less than the degree of the denominator.

Tags

CCSS.HSF-IF.C.7D

Front

What is the horizontal asymptote of the function f(x) = 1/x?

Back

The horizontal asymptote is y = 0.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes can be found by setting the denominator of a rational function equal to zero and solving for x.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

The degree of the numerator and denominator determines the behavior of the function as x approaches infinity and the existence of horizontal asymptotes.

Tags

CCSS.HSF-IF.C.7D

Front

What happens when the degree of the numerator is greater than the degree of the denominator?

Back

If the degree of the numerator is greater than the degree of the denominator, the horizontal asymptote is at y = 0.

Tags

CCSS.HSF-IF.C.7D

Front

What are the possible values for vertical asymptotes in the function f(x) = (x-3)/(x^2-4)?

Back

The vertical asymptotes are x = 2 and x = -2.

Tags

CCSS.HSF-IF.C.7D

Front

What is the vertical asymptote of the function f(x) = 1/(x-3)?

Back

The vertical asymptote is x = 3.

Tags

CCSS.HSF-IF.C.7D