Write the function rule g(x) after the given transformations of the graph of f(x) = 6x. reflection in the x-axis; vertical compression by a factor of - g(x)=
Write the function rule g(x) after the given transformations of the graph of f(x) = 6x. reflection in the x-axis; vertical compression by a factor of - g(x)=
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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![**Educational Content: Transformations of Functions**
**Problem Statement:**
Write the function rule \( g(x) \) after the given transformations of the graph of \( f(x) = 6x \).
Transformations:
1. Reflection in the x-axis
2. Vertical compression by a factor of \( \frac{1}{2} \)
**Solution:**
To find \( g(x) \), apply the transformations step-by-step to the function \( f(x) = 6x \).
1. **Reflection in the x-axis**:
- Reflecting a function in the x-axis involves changing the sign of the function's output. Thus, the reflection of \( f(x) = 6x \) is \( -6x \).
2. **Vertical compression by a factor of \( \frac{1}{2} \)**:
- Compressing a function vertically by \( \frac{1}{2} \) means multiplying the function by \( \frac{1}{2} \). Thus, we multiply \( -6x \) by \( \frac{1}{2} \) to get \( -3x \).
Therefore, the new function rule is:
\[ g(x) = -3x \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa7d34ce-a17c-44ce-a3ca-71da2b3b3b33%2Fa1cfbdec-7d8b-439a-b1e9-89a994e226dc%2Fdqv0mni_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content: Transformations of Functions**
**Problem Statement:**
Write the function rule \( g(x) \) after the given transformations of the graph of \( f(x) = 6x \).
Transformations:
1. Reflection in the x-axis
2. Vertical compression by a factor of \( \frac{1}{2} \)
**Solution:**
To find \( g(x) \), apply the transformations step-by-step to the function \( f(x) = 6x \).
1. **Reflection in the x-axis**:
- Reflecting a function in the x-axis involves changing the sign of the function's output. Thus, the reflection of \( f(x) = 6x \) is \( -6x \).
2. **Vertical compression by a factor of \( \frac{1}{2} \)**:
- Compressing a function vertically by \( \frac{1}{2} \) means multiplying the function by \( \frac{1}{2} \). Thus, we multiply \( -6x \) by \( \frac{1}{2} \) to get \( -3x \).
Therefore, the new function rule is:
\[ g(x) = -3x \]
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