Asymptotes Objective: -Be able to find vertical and horizontal asymptotes.

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Presentation transcript:

Asymptotes Objective: -Be able to find vertical and horizontal asymptotes

Asymptotes: An asymptote is a line or curve that describes the behavior of a graph. The two kinds of asymptotes we will be working with are vertical and horizontal.

Types of Asymptotes Vertical Horizontal x = a y = b

Finding a Vertical Asymptote Vertical asymptotes have an equation of x = a, where a is a value that makes only the denominator equal zero

Examples 1) Find the vertical asymptote(s) of

Examples 2) Find the vertical asymptote(s) of

Examples 3) Find the vertical asymptote(s) of

Examples 4) Find the vertical asymptote(s) of

Finding a Horizontal Asymptote Horizontal asymptotes of a function, f(x), have an equation of y = b, where

Examples 5) Find the horizontal asymptote(s) of

Examples 6) Find the horizontal asymptote(s) of

Examples 7) Find the horizontal asymptote(s) of

Examples 8) Find the horizontal asymptote(s) of

Examples 9) Find the horizontal asymptote(s) of

In summary: We will be working with two types of asymptotes: vertical and horizontal To find a vertical asymptote, find where only the denominator is equal to zero To find a horizontal asymptote, find