EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Question
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
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:
Interpretation:
The above graph represents the sketch of given function.
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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