   Chapter 2.6, Problem 6E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Sketch the graph of an example of a function f that satisfies all of the given conditions. lim x → 2 f ( x ) = ∞ ,   lim x → − 2 + f ( x ) = ∞ ,   lim x → − 2 − f ( x ) = − ∞ ,   lim x → − ∞ f ( x ) = 0 ,   lim x → ∞ f ( x ) = 0 ,   f ( x ) = 0

To determine

To sketch: The graph of f(x) which satisfies the conditions, limx2f(x)=, limx2+f(x)=,limx2f(x)=,limxf(x)=0,limxf(x)=0 and  f(0)=0.

Explanation

Recall the definition of horizontal asymptote, “the line y=L is called a horizontal asymptote of the curve y=f(x) if limxf(x)=L or limxf(x)=L”.

Recall the definition that the line x=a is said to be a vertical asymptote of the function f(x), if at least one of the following conditions must be true:limxaf(x)=±, limxa+f(x)=±, limxaf(x)= and limxaf(x)=.

The limx2f(x)= means that x=2 is a vertical asymptote to the function f

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