Graphing 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

What is the general form of a rational function?

Back

The general form of a rational function is f(x) = P(x) / Q(x), where P(x) and Q(x) are polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the x-intercepts of a rational function?

Back

To find the x-intercepts, set the numerator P(x) equal to zero and solve for x.

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 find vertical asymptotes in a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator Q(x) equal to zero, provided these values do not also make the numerator zero.

Tags

CCSS.HSF-IF.C.7D

Front

What is a hole in a rational function?

Back

A hole occurs at a value of x where both the numerator and denominator are zero, indicating a removable discontinuity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you identify holes in a rational function?

Back

To identify holes, factor both the numerator and denominator, and find common factors that cancel out.

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 positive or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine 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 is a slant (oblique) asymptote?

Back

A slant asymptote occurs when the degree of the numerator is one greater than the degree of the denominator.

Tags

CCSS.HSF-IF.C.7D