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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem

Checkpoint 3 Worked-out solution available at LarsonAppliedCalculus.com

Determine all vertical asymptotes of the graph of

f ( x ) = x 2 + 4 x + 3 x 2 9

To determine

To calculate: The vertical asymptotes of the function f(x)=x2+4x+3x29.

Explanation

Given Information:

The provided function f(x)=x2+4x+3x29.

Formula used:

For vertical asymptote:

If f(x) approaches infinity as x approaches to c from the right or left then the line x=c is a vertical asymptotes of the graph of f(x).

Calculation:

Consider the function,

f(x)=x2+4x+3x29

Simplify further,

f(x)=x2+4x+3x29=(x2+3x+1x+3)(x3)(x+3)=(x(x+1)+1(x+3))(x3)(x+3)=(x+1)(x+3)(x3)(x+3)

Again Simplify further and eliminate all like term:

f(x)=(x+1)(x+3)(x3)(x+3)=(x+1)(x3)

If f(x) approaches infinity as x approaches to c from the right or left then the line x=c is a vertical asymptotes of the graph of f(x).

The graph of f(x)=(x+1)(x3) have the vertical asymptotes when y or y

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