BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015
15th Edition
ISBN: 9781608408405
Author: HOUGHTON MIFFLIN HARCOURT
Publisher: Cengage Learning
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Question
Chapter 6.4, Problem 47E
To determine
To describe the transformation of the graph f and then give the equation of the asymptote.
Expert Solution & Answer
Answer to Problem 47E
The graph of the function f(x) is shifted left by 6 units. The required equation of the asymptote is x=−6 .
Explanation of Solution
Given information:
The given the function f(x) and the transformed function g(x) are given as f(x)=lnxand g(x)=ln(x+6).
Calculation:
Consider the given function f(x) as f(x)=lnx
It can be seen that the transformed graph g(x) can be obtained by adding 6 in the x− coordinate of the function f(x) .
f(x+6)=ln(x+6)
f(x+6)=g(x)
On adding 6 in the x− coordinate of the function of f(x) , the graph of f(x) is shifted left by 6 units.
The function f(x)=lnx has a vertical asymptote x=0 , as the graph of f(x) is shifted left by 6 units, the asymptote of the graph is also shifted left by 6 units. Then the asymptote to the graph of the function g(x) is given as x=−6 .
The graph of the function g(x) and its asymptote is given below in the graph.
Hence, the equation of the asymptote is x=−6 .
Chapter 6 Solutions
BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015
Ch. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.1 - Prob. 8ECh. 6.1 - Prob. 9ECh. 6.1 - Prob. 10E
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