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5. A function y = sin x is transformed into = -sin (3x) - 4. What is a possible transformation?

5. A function y = sin x is transformed into = -sin (3x) - 4. What is a possible transformation?

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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**Exercise 5: Function Transformation** A function \( y = \sin x \) is transformed into \( y' = -\sin(3x) - 4 \). **Question:** What is a possible transformation? **Explanation:** 1. **Reflection**: The negative sign in front of the function indicates a reflection across the x-axis. 2. **Horizontal Compression**: The factor of 3 within the sine function indicates a horizontal compression by a factor of \(\frac{1}{3}\). 3. **Vertical Shift**: The subtraction of 4 indicates a vertical shift downwards by 4 units. Overall, the transformation consists of reflecting the sine wave across the x-axis, compressing it horizontally, and shifting it downwards.
Transcribed Image Text:**Exercise 5: Function Transformation** A function \( y = \sin x \) is transformed into \( y' = -\sin(3x) - 4 \). **Question:** What is a possible transformation? **Explanation:** 1. **Reflection**: The negative sign in front of the function indicates a reflection across the x-axis. 2. **Horizontal Compression**: The factor of 3 within the sine function indicates a horizontal compression by a factor of \(\frac{1}{3}\). 3. **Vertical Shift**: The subtraction of 4 indicates a vertical shift downwards by 4 units. Overall, the transformation consists of reflecting the sine wave across the x-axis, compressing it horizontally, and shifting it downwards.
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