Rational Function Graphs Review

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

Define x-intercept (zero) of a function.

Back

The x-intercept (or zero) of a function is the point where the graph of the function crosses the x-axis, meaning the output (y-value) is zero.

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 of the rational function 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 vertical 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 vertical asymptotes in a rational function?

Back

Vertical asymptotes occur at values of x that make the denominator zero, provided the numerator is not also zero at those points.

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 of a function approaches as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes in rational functions?

Back

To find horizontal asymptotes, 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

If the degree of the numerator is less than the degree of the denominator, 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

If the degrees are equal, the horizontal asymptote is y = the ratio of the leading coefficients of the numerator and 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

If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote; the function may have an oblique asymptote.

Tags

CCSS.HSF-IF.C.7D