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A function is transformed from f (x) = 7 to g(x) = 7(4), What is the effect on f(x)? Horizontal Compression by a factor of 1/4 Vertical Compression by a factor of 1/4 Vertical Stretch by a factor of 4 Horizontal Stretch by a factor of 4

A function is transformed from f (x) = 7 to g(x) = 7(4), What is the effect on f(x)? Horizontal Compression by a factor of 1/4 Vertical Compression by a factor of 1/4 Vertical Stretch by a factor of 4 Horizontal Stretch by a factor of 4

Algebra and Trigonometry (6th Edition)
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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### Understanding Function Transformations When a function is transformed from \( f(x) = 7^x \) to \( g(x) = 7^{(4x)} \), what is the effect on \( f(x) \)? - ○ Horizontal Compression by a factor of 1/4 - ○ Vertical Compression by a factor of 1/4 - ○ Vertical Stretch by a factor of 4 - ○ Horizontal Stretch by a factor of 4 #### Explanation This transformation involves modifying the exponent of the base function \( 7^x \). Specifically, \( 7^x \) becomes \( 7^{4x} \). This exponentiation implies a horizontal transformation due to the coefficient of \( x \). 1. The transformation \( 7^{4x} \) compresses the graph horizontally by a factor of \( \frac{1}{4} \). This means for any given value of \( x \), the function \( g(x) \) reaches the same output as \( f(x) \) does, but at \( x \) scaled down by a factor of 4. Here, we choose the correct understanding of transformations: - **Horizontal Compression by a factor of 1/4** Ensure you consider the base transformation types and how coefficients inside the function arguments affect the graph shape and orientation. For more detailed explanations, please refer to the transformations chapter of your mathematics textbook.
Transcribed Image Text:### Understanding Function Transformations When a function is transformed from \( f(x) = 7^x \) to \( g(x) = 7^{(4x)} \), what is the effect on \( f(x) \)? - ○ Horizontal Compression by a factor of 1/4 - ○ Vertical Compression by a factor of 1/4 - ○ Vertical Stretch by a factor of 4 - ○ Horizontal Stretch by a factor of 4 #### Explanation This transformation involves modifying the exponent of the base function \( 7^x \). Specifically, \( 7^x \) becomes \( 7^{4x} \). This exponentiation implies a horizontal transformation due to the coefficient of \( x \). 1. The transformation \( 7^{4x} \) compresses the graph horizontally by a factor of \( \frac{1}{4} \). This means for any given value of \( x \), the function \( g(x) \) reaches the same output as \( f(x) \) does, but at \( x \) scaled down by a factor of 4. Here, we choose the correct understanding of transformations: - **Horizontal Compression by a factor of 1/4** Ensure you consider the base transformation types and how coefficients inside the function arguments affect the graph shape and orientation. For more detailed explanations, please refer to the transformations chapter of your mathematics textbook.
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