Suppose f(x) = √. Give the function for each of the following transformations. The graph of f(x) reflected across the x-axis. Of(x) = -√ Of(x) = Of(x) = -x -√√√x The graph of f(x) shifted right 5 units Of(x)=√x - 5 Of(x)=√x + 5 Of(x) = √√x + 5 Of(x)=√x - 5 The graph of f(x) shifted down 1 units Of(x)=√x+1 Of(x)=√x - 1 Of(x)=√x-1 Of(x)=√x+1 The graph of f(x) shifted left 5 units and shifted up 1 units. Of(x) = √√√x + 5+1 Of(x)=√x+5-1 Of(x)=√x-5-1 Of(x) = √√x - 5+1 The graph of f(x) stretched vertically by a factor of 5. Of(x) = √5x 1 Of(x) = 5 ○ f(x) = -√√√x Of(x) = 5√x
Suppose f(x) = √. Give the function for each of the following transformations. The graph of f(x) reflected across the x-axis. Of(x) = -√ Of(x) = Of(x) = -x -√√√x The graph of f(x) shifted right 5 units Of(x)=√x - 5 Of(x)=√x + 5 Of(x) = √√x + 5 Of(x)=√x - 5 The graph of f(x) shifted down 1 units Of(x)=√x+1 Of(x)=√x - 1 Of(x)=√x-1 Of(x)=√x+1 The graph of f(x) shifted left 5 units and shifted up 1 units. Of(x) = √√√x + 5+1 Of(x)=√x+5-1 Of(x)=√x-5-1 Of(x) = √√x - 5+1 The graph of f(x) stretched vertically by a factor of 5. Of(x) = √5x 1 Of(x) = 5 ○ f(x) = -√√√x Of(x) = 5√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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Transcribed Image Text:**Title:** Transformations of the Square Root Function
Suppose \( f(x) = \sqrt{x} \). Identify the function for each of the following transformations.
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### Transformation Descriptions and Options
**1. The graph of \( f(x) \) reflected across the x-axis.**
- \( f(x) = -\sqrt{x} \)
- \( f(x) = -\sqrt{-x} \)
- \( f(x) = \sqrt{-x} \)
**2. The graph of \( f(x) \) shifted right 5 units.**
- \( f(x) = \sqrt{x-5} \)
- \( f(x) = \sqrt{x+5} \)
- \( f(x) = \sqrt{x}+5 \)
- \( f(x) = \sqrt{x}-5 \)
**3. The graph of \( f(x) \) shifted down 1 unit.**
- \( f(x) = \sqrt{x}+1 \)
- \( f(x) = \sqrt{x}-1 \)
- \( f(x) = \sqrt{x+1} \)
- \( f(x) = \sqrt{x-1} \)
**4. The graph of \( f(x) \) shifted left 5 units and shifted up 1 unit.**
- \( f(x) = \sqrt{x+5}+1 \)
- \( f(x) = \sqrt{x+5}-1 \)
- \( f(x) = \sqrt{x-5}-1 \)
- \( f(x) = \sqrt{x-5}+1 \)
**5. The graph of \( f(x) \) stretched vertically by a factor of 5.**
- \( f(x) = \sqrt{5x} \)
- \( f(x) = \sqrt{\frac{1}{5}x} \)
- \( f(x) = \frac{1}{5}\sqrt{x} \)
- \( f(x) = 5\sqrt{x} \)
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