EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Chapter 3, Problem 27CLT
To determine

To draw: The graph of the rational function f(x)=x3−2x2−9x+18x2+4x+3 . Also identify all intercepts and find all asymptotes.

Expert Solution & Answer
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Answer to Problem 27CLT

x − intercept are 2,3 and y − intercept is 6. x=−1 is the asymptote.

Explanation of Solution

Given information:

Given rational function is, f(x)=x3−2x2−9x+18x2+4x+3 .

Consider, the given rational function as f(x)=x3−2x2−9x+18x2+4x+3 .

Graph of the function is,

  EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 27CLT

From the graph it can be observed that the curve cuts the x − axis only at x=2 and x=3 and y − axis at y=6

Hence, the x − intercept are 2,3 and y − intercept is 6.

Also, the function f(x)=x3−2x2−9x+18x2+4x+3 can be written as

  f(x)=x2(x−2)−9(x+2)x2+3x+x+3=(x−2)(x2−9)(x+3)(x+1)=(x−2)(x−3)(x+3)(x+3)(x+1)=(x−2)(x−3)(x+1)

This implies that the function is not defined at x=−1 .

The asymptote of the function is x=−1

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Chapter 3, Problem 26CLT
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Chapter 3, Problem 28CLT

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
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