Rational Functions

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 is a vertical asymptote?

Back

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

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 line y = b that the function 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

Horizontal asymptotes can be determined by comparing the degrees of the numerator and denominator polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

What does it mean if a rational function has no vertical asymptotes?

Back

If a rational function has no vertical asymptotes, it means the denominator does not have any real roots.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

The y-intercept indicates the point where the graph of the function crosses the y-axis.

Tags

CCSS.HSF-IF.C.7D

Front

How can you identify holes in the graph of a rational function?

Back

Holes occur at values of x that make both the numerator and denominator zero; these points are not included in the function.

Tags

CCSS.HSF-IF.C.7D

Front

What is the end behavior of a rational function?

Back

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

Tags

CCSS.HSF-IF.C.7D