Precalc Unit 2 Flashcardizz

Front

What is a slant asymptote?

Back

A slant asymptote is a diagonal line that a graph approaches as x approaches infinity or negative infinity. It occurs when the degree of the numerator is one more than the degree of the denominator in a rational function.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the equation of a slant asymptote?

Back

To find the equation of a slant asymptote, perform polynomial long division on the rational function. The quotient (ignoring the remainder) gives the equation of the slant asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = a where a function approaches infinity or negative infinity. It occurs at values of x that make the denominator of a rational function equal to zero.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find vertical asymptotes?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Tags

CCSS.HSF-IF.C.7D

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line y = b that a graph approaches as x approaches infinity or negative infinity. It indicates the end behavior of the function.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes?

Back

To find horizontal asymptotes, compare the degrees of the numerator and denominator: If the degree of the numerator is less, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, there is no horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of asymptotes in graphing?

Back

Asymptotes help determine the behavior of a graph near certain values and guide the overall shape of the graph, indicating where the function does not exist or approaches infinity.

Tags

CCSS.HSF-IF.C.7D

Front

What is the equation of the slant asymptote for the function f(x) = (2x^2 + 3x + 1)/(x + 1)?

Back

The slant asymptote is y = 2x + 1.

Tags

CCSS.HSF-IF.C.7D

Front

What is the equation of the slant asymptote for the function f(x) = (x^3 + 2x^2 + 3)/(x^2 + 1)?

Back

The slant asymptote is y = x.

Tags

CCSS.HSF-IF.C.7D

Front

What are the asymptotes of the function f(x) = (x^2 - 4)/(x^2 - 1)?

Back

The vertical asymptotes are x = 1 and x = -1; the horizontal asymptote is y = 1.

Tags

CCSS.HSF-IF.C.7D