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,...
Related questions
Question
Need to know if it’s A B C OR D
![### Exploring Function Transformations: Horizontal Stretching
#### Question:
Which function shows \( f(x) = 6^x \) being horizontally stretched by a factor of 4?
#### Options:
- **Option 1:**
\[
\bigcirc \quad f(x) = 6^{(4x)}
\]
- **Option 2:**
\[
\bigcirc \quad f(x) = \frac{1}{4} \cdot 6^x
\]
- **Option 3:**
\[
\bigcirc \quad f(x) = 4 \cdot 6^x
\]
- **Option 4:**
\[
\bigcirc \quad f(x) = 6^{(\frac{1}{4}x)}
\]
#### Explanation:
To stretch the function \( f(x) = 6^x \) horizontally by a factor of 4, we need to replace \( x \) with \( \frac{x}{4} \). This transformation compresses the horizontal distance each point on the graph travels from the y-axis by a factor of 4.
The correct function should thus be:
\[
f(x) = 6^{(\frac{1}{4}x)}
\]
Hence, the correct option is the fourth one.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45e4ee6c-a715-4803-9fbe-92a41a442b45%2Ff6de0f6a-0a28-42e5-978f-df28e98b4131%2F4wn39zj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Exploring Function Transformations: Horizontal Stretching
#### Question:
Which function shows \( f(x) = 6^x \) being horizontally stretched by a factor of 4?
#### Options:
- **Option 1:**
\[
\bigcirc \quad f(x) = 6^{(4x)}
\]
- **Option 2:**
\[
\bigcirc \quad f(x) = \frac{1}{4} \cdot 6^x
\]
- **Option 3:**
\[
\bigcirc \quad f(x) = 4 \cdot 6^x
\]
- **Option 4:**
\[
\bigcirc \quad f(x) = 6^{(\frac{1}{4}x)}
\]
#### Explanation:
To stretch the function \( f(x) = 6^x \) horizontally by a factor of 4, we need to replace \( x \) with \( \frac{x}{4} \). This transformation compresses the horizontal distance each point on the graph travels from the y-axis by a factor of 4.
The correct function should thus be:
\[
f(x) = 6^{(\frac{1}{4}x)}
\]
Hence, the correct option is the fourth one.
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