RVHS Graphing Rational Functions Review

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the ratio of two polynomials, typically in the form f(x) = P(x)/Q(x), where P and Q are polynomials.

Tags

CCSS.HSF-IF.C.7D

Front

What determines the vertical asymptotes of a rational function?

Back

Vertical asymptotes are determined by the values of x that make the denominator Q(x) equal to zero, provided that these values do not also make the numerator P(x) equal to zero.

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

Back

The degree of the numerator and denominator determines the behavior of the function, including the existence of horizontal asymptotes.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

If the degrees are equal, the horizontal asymptote is y = leading coefficient of P(x) / leading coefficient of Q(x).

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 exactly one more than the degree of the denominator.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the vertical asymptotes of the function f(x) = (x^2 - 4)/(x^2 - 1)?

Back

Set the denominator x^2 - 1 equal to zero. The vertical asymptotes are at x = 1 and x = -1.

Tags

CCSS.HSF-IF.C.7D

Front

What is the formula for finding the horizontal asymptote of a rational function?

Back

The horizontal asymptote can be found using the degrees of the numerator and denominator: if degree of numerator < degree of denominator, y=0; if equal, y= leading coefficient of P / leading coefficient of Q.

Tags

CCSS.HSF-IF.C.7D