FLASHCARD Graphing Rational Functions

Front

What is a rational function?

Back

A function that can be expressed as the ratio of two polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

What is the general form of a rational function?

Back

f(x) = P(x) / Q(x), where P and Q are polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

What is an asymptote?

Back

A line that a graph approaches but never crosses.

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

A horizontal line that a graph approaches as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes for rational functions?

Back

Compare the degrees of the numerator and denominator polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

What happens if the degree of the numerator is less than the degree of the denominator?

Back

The horizontal asymptote is y = 0.

Tags

CCSS.HSF-IF.C.7D

Front

What happens if the degree of the numerator is equal to the degree of the denominator?

Back

The horizontal asymptote is y = leading coefficient of numerator / leading coefficient of denominator.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

There is no horizontal asymptote; the graph may have an oblique asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of vertical asymptotes?

Back

They indicate values of x where the function is undefined.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes for rational functions?

Back

Set the denominator equal to zero and solve for x.

Tags

CCSS.HSF-IF.C.7D