Which of the following is true? gs (PE xMail -RIGGINS, DIMITRI - Outlool XS Savvas Realizeavwasrealize.com/community/classes/563d20c74b934625bb83249538be8129/assignments/ee7d527a4e974aea8afac55da4The logarithmic function f(x) = log x is transformed to g(x) = log(x+ 1) + 3. Which of the following is true?A. f(x) is translated 1 unit upward.B. f(X) is translated 3 units downward.C. The vertical asymptote shifts 1 unit to the left.D. The vertical asymptote shifts 3 units to the right.

Name: Which of the following is true? gs (PE xMail -RIGGINS, DIMITRI - Outlo
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Description: Which of the following is true? gs (PE xMail -RIGGINS, DIMITRI - Outlool XS Savvas Realizeavwasrealize.com/community/classes/563d20c74b934625bb83249538be8129/assignments/ee7d527a4e974aea8afac55da4The logarithmic function f(x) = log x is transformed t

Answered: The logarithmic function f(x) = log x…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Which of the following is true?

gs (PE x
Mail -RIGGINS, DIMITRI - Outlool X
S Savvas Realize
avwasrealize.com/community/classes/563d20c74b934625bb83249538be8129/assignments/ee7d527a4e974aea8afac55da4
The logarithmic function f(x) = log x is transformed to g(x) = log(x+ 1) + 3. Which of the following is true?
A. f(x) is translated 1 unit upward.
B. f(X) is translated 3 units downward.
C. The vertical asymptote shifts 1 unit to the left.
D. The vertical asymptote shifts 3 units to the right.

Expert Solution

Step 1: Basic information

Concept used.

1. Horizontal shift:

f(x+c) is horizontally shifted w.r.t f(x) by c units.

If c < 0, then shift is right wards w.r.t f(x) .

If c > 0, then shift is left wards w.r.t f(x).

2. Vertical shift:

f(x) + c is a vertical shift w.r.t. f(x).

If c < 0, then shift is downwards w.r.t f(x) .

If c > 0, then shift is upwards w.r.t f(x).

Given:

f(x) = log(x)

Key point:

The function has vertical asymptotes at x = 0 as log(x) approaches -ve infinity at x = 0.

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