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1 cos (2x) Graph f(x) = sin ²x = for 0

1 cos (2x) Graph f(x) = sin ²x = for 0

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
**Function Analysis and Graphing** **Function Description:** Graph \( f(x) = \sin^2(x) = \frac{1 - \cos(2x)}{2} \) for \( 0 \leq x \leq 2\pi \) by using transformations. **Analysis Requirements:** Please provide the following information about the function: - **Amplitude:** Determine the amplitude of the function. - **Vertical Shift:** Identify any vertical shift present. - **Horizontal Shift:** Determine any horizontal shift that applies. - **Period:** Calculate the period of the function if necessary. **Function Explanation:** The function given is \( f(x) = \sin^2(x) \), which can be rewritten using the double-angle identity for cosine as \( f(x) = \frac{1 - \cos(2x)}{2} \). This form is often used for graphing trigonometric transformations. --- **Note:** When teaching or learning about this function, focus on understanding the transformation properties that lead to identifying the amplitude, shifts, and period effectively.
Transcribed Image Text:**Function Analysis and Graphing** **Function Description:** Graph \( f(x) = \sin^2(x) = \frac{1 - \cos(2x)}{2} \) for \( 0 \leq x \leq 2\pi \) by using transformations. **Analysis Requirements:** Please provide the following information about the function: - **Amplitude:** Determine the amplitude of the function. - **Vertical Shift:** Identify any vertical shift present. - **Horizontal Shift:** Determine any horizontal shift that applies. - **Period:** Calculate the period of the function if necessary. **Function Explanation:** The function given is \( f(x) = \sin^2(x) \), which can be rewritten using the double-angle identity for cosine as \( f(x) = \frac{1 - \cos(2x)}{2} \). This form is often used for graphing trigonometric transformations. --- **Note:** When teaching or learning about this function, focus on understanding the transformation properties that lead to identifying the amplitude, shifts, and period effectively.
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