PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
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Chapter 3.2, Problem 90E
To determine

To find:

The domain, vertical asymptote, and x -intercept of the given logarithmic function. Sketch the graph of function.

Expert Solution & Answer
Check Mark

Answer to Problem 90E

Domain: (−1,∞) ,

Vertical asymptote: x=−1 ,

The x -intercept: (0,0) .

Explanation of Solution

Given:

A logarithm function: h(x)=ln(x+1).

Calculation:

We know that logarithmic functions are not defined for negative values. To find domain of our given function, we will set argument of log function greater than 0 as:

  x+1>0x>−1

Therefore, the domain of our given logarithmic function would be x>−1 or (−1,∞).

We know that logarithmic functions are not defined at 0. To find vertical asymptote, we will set argument of logarithmic function equal to 0 as:

  x+1=0x=−1

Therefore, the given logarithmic function has a vertical asymptote at x=−1.

To find the x -intercept of our given function, we will set y=0 and solve for x as:

  ln(x+1)=0e0=x+1 (Converting log to exponetial form)1=x+10=x

Therefore, the x- intercept of our given logarithmic function is (0,0).

Upon graphing our given logarithmic function, we will get our required graph as shown below:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 90E

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Chapter 3 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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Prob. 27CTCh. 3 - Prob. 28CTCh. 3 - Prob. 29CTCh. 3 - Prob. 30CTCh. 3 - Prob. 1STPCh. 3 - Prob. 2STPCh. 3 - Prob. 3STPCh. 3 - Prob. 4STPCh. 3 - Prob. 5STPCh. 3 - Prob. 6STPCh. 3 - Prob. 7STPCh. 3 - Prob. 8STPCh. 3 - Prob. 9STPCh. 3 - Prob. 10STPCh. 3 - Prob. 11STPCh. 3 - Prob. 12STPCh. 3 - Prob. 13STPCh. 3 - Prob. 14STPCh. 3 - Prob. 15STPCh. 3 - Prob. 16STPCh. 3 - Prob. 17STPCh. 3 - Prob. 18STPCh. 3 - Prob. 19STPCh. 3 - Prob. 20STPCh. 3 - Prob. 21STPCh. 3 - Prob. 22STPCh. 3 - Prob. 23STPCh. 3 - Prob. 24STPCh. 3 - Prob. 25STPCh. 3 - Prob. 26STP
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