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17 Describe the effect on the function f(x) = √x to g(x)=√x-2. F The graph was a vertical compression and a horizontal shift right. G H The graph was a vertical stretch and a horizontal shift right. The graph was a vertical compression and a horizontal shift left. 1 The graph was a vertical stretch and a horizontal shift right.

17 Describe the effect on the function f(x) = √x to g(x)=√x-2. F The graph was a vertical compression and a horizontal shift right. G H The graph was a vertical stretch and a horizontal shift right. The graph was a vertical compression and a horizontal shift left. 1 The graph was a vertical stretch and a horizontal shift right.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Question 17: Transformation of Functions #### Describe the effect on the function \( f(x) = \sqrt{x} \) to \( g(x) = \frac{1}{2} \sqrt{x} - 2 \). Options: - **F**: The graph was a vertical compression and a horizontal shift right. - **G**: The graph was a vertical stretch and a horizontal shift right. - **H**: The graph was a vertical compression and a horizontal shift left. - **J**: The graph was a vertical stretch and a horizontal shift left. #### Analysis: To understand the transformation, we need to break down \( g(x) = \frac{1}{2} \sqrt{x} - 2 \): 1. **Vertical Compression**: The factor \(\frac{1}{2}\) in front of \(\sqrt{x}\) indicates a vertical compression by a factor of 2. 2. **Horizontal Shift**: There is no horizontal shift affecting \( x \) as there is no term added or subtracted inside the square root. 3. **Vertical Shift**: The term \(-2\) indicates a vertical shift downward by 2 units. Combining all these observations, we conclude that \( g(x) \) represents a vertical compression by a factor of \(\frac{1}{2}\) and a vertical shift downward by 2 units. However, there might be a misunderstanding in the provided choices. Ensure further study of linear transformation descriptions to clear confusions, especially on the clarity and correctness of option texts.
Transcribed Image Text:### Question 17: Transformation of Functions #### Describe the effect on the function \( f(x) = \sqrt{x} \) to \( g(x) = \frac{1}{2} \sqrt{x} - 2 \). Options: - **F**: The graph was a vertical compression and a horizontal shift right. - **G**: The graph was a vertical stretch and a horizontal shift right. - **H**: The graph was a vertical compression and a horizontal shift left. - **J**: The graph was a vertical stretch and a horizontal shift left. #### Analysis: To understand the transformation, we need to break down \( g(x) = \frac{1}{2} \sqrt{x} - 2 \): 1. **Vertical Compression**: The factor \(\frac{1}{2}\) in front of \(\sqrt{x}\) indicates a vertical compression by a factor of 2. 2. **Horizontal Shift**: There is no horizontal shift affecting \( x \) as there is no term added or subtracted inside the square root. 3. **Vertical Shift**: The term \(-2\) indicates a vertical shift downward by 2 units. Combining all these observations, we conclude that \( g(x) \) represents a vertical compression by a factor of \(\frac{1}{2}\) and a vertical shift downward by 2 units. However, there might be a misunderstanding in the provided choices. Ensure further study of linear transformation descriptions to clear confusions, especially on the clarity and correctness of option texts.
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