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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Chapter 3.2, Problem 47E
To determine

To find: the domain, x-intercept, and vertical asymptote of the given logarithmic function and graph it.

Expert Solution & Answer
Check Mark

Answer to Problem 47E

For y=1+log10x

Domain:  x>0

The x-intercept: (110,0)

The vertical asymptote: x=0 .

The graph:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 47E , additional homework tip 1

Explanation of Solution

Given information:

The given logarithmic function:

  y=1+log10x

Calculation:

As per problem,

For the function: y=1+log10x

1. Domain:

Because log10x is defined only when x>0

So, the domain of the function y is  x>0 .

2. Find the x-intercept:

  1+log10x=0       [Set y=0]    log10x=−1     [Subtract 1 from each side]             x=10−1   [Write in exponential form]             x=110 

The x-intercept is at (110,0)

3. Find the vertical asymptote:

  x=0     [Set x=0]

The vertical asymptote is x=0 .

The graph of y=1+log10x :

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 3.2, Problem 47E , additional homework tip 2

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Chapter 3.2, Problem 46E
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Chapter 3.2, Problem 48E

Chapter 3 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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SEE MORE TEXTBOOKS
Implicit Differentiation with Transcendental Functions; Author: Mathispower4u;https://www.youtube.com/watch?v=16WoO59R88w;License: Standard YouTube License, CC-BY
How to determine the difference between an algebraic and transcendental expression; Author: Study Force;https://www.youtube.com/watch?v=xRht10w7ZOE;License: Standard YouTube License, CC-BY