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1 Given f(x) = |x| & g (x) = 5f (æ) 2 Describe the transformation from f(x) to g(x)

1 Given f(x) = |x| & g (x) = 5f (æ) 2 Describe the transformation from f(x) to g(x)

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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### Given Functions and Transformations #### Overview The provided mathematical functions and transformation are as follows: - Given \( f(x) = |x| \) - Another function \( g(x) = \frac{1}{2}f(x) - 4.5 \) #### Description of Transformation The transformation from \( f(x) \) to \( g(x) \) involves the following steps: 1. **Vertical Compression**: The function \( f(x) \), which is the absolute value function \( |x| \), is vertically compressed by a factor of \( \frac{1}{2} \). This means that for every output value of \( f(x) \), the corresponding value of \( g(x) \) will be half as large. 2. **Vertical Translation**: After the initial compression, the resulting function is then shifted downwards by 4.5 units. This translates every point on the function \( \frac{1}{2} |x| \) downward along the y-axis by 4.5 units. By understanding these transformations, learners can visualize and analyze how the original absolute value function \( f(x) \) is altered to produce \( g(x) \).
Transcribed Image Text:### Given Functions and Transformations #### Overview The provided mathematical functions and transformation are as follows: - Given \( f(x) = |x| \) - Another function \( g(x) = \frac{1}{2}f(x) - 4.5 \) #### Description of Transformation The transformation from \( f(x) \) to \( g(x) \) involves the following steps: 1. **Vertical Compression**: The function \( f(x) \), which is the absolute value function \( |x| \), is vertically compressed by a factor of \( \frac{1}{2} \). This means that for every output value of \( f(x) \), the corresponding value of \( g(x) \) will be half as large. 2. **Vertical Translation**: After the initial compression, the resulting function is then shifted downwards by 4.5 units. This translates every point on the function \( \frac{1}{2} |x| \) downward along the y-axis by 4.5 units. By understanding these transformations, learners can visualize and analyze how the original absolute value function \( f(x) \) is altered to produce \( g(x) \).
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