   Chapter 2.6, Problem 8E

Chapter
Section
Textbook Problem

Sketch the graph of an example of a function f that satisfies all of the given conditions. lim x → ∞ f ( x ) = 3 ,   lim x → 2 − f ( x ) = ∞ ,   lim x → 2 + f ( x ) = − ∞ ,   f   is odd

To determine

To sketch: The graph of f(x) which satisfies the conditions, limxf(x)=3, limx2f(x)=, limx2+f(x)= and f is odd.

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 limxf(x)=3 means that y=3 is a horizontal asymptote to the function f as x approaches infinity.

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

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