Precalculus with Limits
Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 3.2, Problem 45E
To determine

To find the domain, x - intercepts, vertical asymptotes and to sketch the graph of the function

  f(x)=−log6(x+2) .

Expert Solution & Answer
Check Mark

Answer to Problem 45E

  (−2,∞)

Explanation of Solution

Given:

Function: f(x)=−log6(x+2)

Formula used:

  logab=c⇔b=ac

Calculation:

Finding the domain of the function,

When x>−2 , the function is defined.

So, the domain of the function is (−2,∞).

To find the x-intercept, put f(x)=y=0 in given function.

  ⇒0=−log6(x+2)⇒0=log6(x+2)⇒x+2=60          [∵logab=c⇔b=ac]⇒x+2=1⇒x=1−2⇒x=−1

So, x-intercept is (−1,0) .

Asymptotes:

Vertical asymptotes:

To find vertical asymptotes, put the value of the given function in logarithmic part equal to zero.

  ⇒x+2=0⇒x=−2

So, the vertical asymptote is x=−2.

Calculation for graph:

Consider f(x)=−log6(x+2)

    Values of x Values of f (x)
    -1 0
    0 -0.387
    1 -0.613
    2 -0.774

By taking different values of x, the graph can be plotted.

Graph:

  Precalculus with Limits, Chapter 3.2, Problem 45E

Interpretation:

The above graph represents the sketch of given function.

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Chapter 3.2, Problem 44E
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Chapter 3.2, Problem 46E

Chapter 3 Solutions

Precalculus with 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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