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.

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.

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.

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.

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.

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.

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.

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.

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.

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.