Rational Function Graphs

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.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the y-intercept of a rational function?

Back

To find the y-intercept, set x = 0 in the function and solve for y.

Tags

CCSS.HSF-IF.C.7D

Front

What does it mean if a rational function has a vertical asymptote?

Back

A vertical asymptote indicates that the function approaches infinity or negative infinity as it gets close to a certain x-value, where the function is undefined.

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine the vertical asymptotes of a rational function?

Back

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

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of the degree of the numerator and denominator in a rational function?

Back

The degree of the numerator and denominator helps determine the behavior of the function at infinity and the existence of horizontal asymptotes.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

Front

What is the relationship between the y-intercept and the function's value at x=0?

Back

The y-intercept is the value of the function when x=0, represented as (0, f(0)).

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if a rational function has no y-intercept?

Back

If a rational function has no y-intercept, it means that the function is undefined at x=0.

Tags

CCSS.HSF.BF.B.3