### Understanding Function TransformationsConsider the function $ f(x) = \log x $. We want to match each transformation of $ f $ with its description from the options provided. #### Descriptions of Transformations:1. **Vertical translation** 2 units up2. **Vertical shrink** by a factor of $ \frac{1}{2} $3. **Horizontal translation** 2 units left4. **Reflection** in the x-axis #### Transformed Functions:- $ g(x) = \frac{1}{2} \log x $- $ h(x) = \log (x + 2) $- $ m(x) = -\log x $- $ n(x) = \log x + 2 $#### Matching Functions to Descriptions:1. **Vertical translation 2 units up:** - $ n(x) = \log x + 2 $2. **Vertical shrink by a factor of $ \frac{1}{2} $:** - $ g(x) = \frac{1}{2} \log x $3. **Horizontal translation 2 units left:** - $ h(x) = \log (x + 2) $4. **Reflection in the x-axis:** - $ m(x) = -\log x $### Explanation of Graphs or Diagrams:This educational exercise involves connecting mathematical expressions to their respective transformations. The diagram shows four descriptions linked by lines to their corresponding transformed functions, reflecting an understanding of how changes in the function's equation translate to geometric transformations on its graph.

Answered: Image /qna-images/answer/038afb7f-6101-4ff7-bb1c-8f14fda92d17.jpg

2/2 Let f(x) = log x. Match each transformation of f with its description. Vertical translation 2 units up Vertical shrink by a factor of Horizontal translation 2 units left Reflection in the x -axis : g(x) = log x : h(x) = log x+2 :: m(x) = -log x | :: n(x) = log(x + 2)

2/2 Let f(x) = log x. Match each transformation of f with its description. Vertical translation 2 units up Vertical shrink by a factor of Horizontal translation 2 units left Reflection in the x -axis : g(x) = log x : h(x) = log x+2 :: m(x) = -log x | :: n(x) = log(x + 2)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

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

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Question

### Understanding Function Transformations

Consider the function $ f(x) = \log x $. We want to match each transformation of $ f $ with its description from the options provided.

#### Descriptions of Transformations:

1. **Vertical translation** 2 units up
2. **Vertical shrink** by a factor of $ \frac{1}{2} $
3. **Horizontal translation** 2 units left
4. **Reflection** in the x-axis

#### Transformed Functions:

- $ g(x) = \frac{1}{2} \log x $
- $ h(x) = \log (x + 2) $
- $ m(x) = -\log x $
- $ n(x) = \log x + 2 $

#### Matching Functions to Descriptions:

1. **Vertical translation 2 units up:**
- $ n(x) = \log x + 2 $

2. **Vertical shrink by a factor of $ \frac{1}{2} $:**
- $ g(x) = \frac{1}{2} \log x $

3. **Horizontal translation 2 units left:**
- $ h(x) = \log (x + 2) $

4. **Reflection in the x-axis:**
- $ m(x) = -\log x $

### Explanation of Graphs or Diagrams:

This educational exercise involves connecting mathematical expressions to their respective transformations. The diagram shows four descriptions linked by lines to their corresponding transformed functions, reflecting an understanding of how changes in the function's equation translate to geometric transformations on its graph.

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