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-3n/4 -12 -1/4 3n /4 5n/4 3n 2 71/4

-3n/4 -12 -1/4 3n /4 5n/4 3n 2 71/4

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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Two sinusoidal functions are graphed below: the graph f(x) green line, and the graph of g(x) is the blue line. Find the following values of the function h(x)= f(x) - g(x) h(-π/2)= h(0)= h(π/2)= h(π)=
The image displays two sinusoidal graphs on a coordinate plane. ### Graph Features: 1. **Axes**: - The horizontal axis (x-axis) is labeled with values in terms of \(\pi\), ranging from \(-3\pi/4\) to \(7\pi/4\). - The vertical axis (y-axis) is labeled with integer values from \(-4\) to \(4\). 2. **Curves**: - The **first curve (green)**: - This is a sinusoidal wave starting at the top left corner. - It decreases from an initial positive value, crosses the x-axis shortly after \(\pi/2\), reaches a minimum around \(\pi\), and increases to a maximum positive value by \(7\pi/4\). - The **second curve (blue)**: - This wave starts from the mid-left above the x-axis, reaching its peak just before \(\pi/4\), crosses the x-axis near \(\pi/2\), reaches a minimum around \(3\pi/2\), and ascends, peaking just before \(2\pi\). ### Graph Analysis: - **Wave Patterns**: - Both curves exhibit typical wave patterns with periodic increases and decreases. - The curves appear out of phase, with peaks and troughs occurring at different x-values. - **Intersection Points**: - The curves intersect in intervals, notably around \(x = 0\) and \(x = \pi\). These sinusoidal graphs can represent various wave-related phenomena such as sound waves, light waves, or alternating current in electrical circuits. Their properties, such as frequency and amplitude, can be analyzed from their periodicity and height.
Transcribed Image Text:The image displays two sinusoidal graphs on a coordinate plane. ### Graph Features: 1. **Axes**: - The horizontal axis (x-axis) is labeled with values in terms of \(\pi\), ranging from \(-3\pi/4\) to \(7\pi/4\). - The vertical axis (y-axis) is labeled with integer values from \(-4\) to \(4\). 2. **Curves**: - The **first curve (green)**: - This is a sinusoidal wave starting at the top left corner. - It decreases from an initial positive value, crosses the x-axis shortly after \(\pi/2\), reaches a minimum around \(\pi\), and increases to a maximum positive value by \(7\pi/4\). - The **second curve (blue)**: - This wave starts from the mid-left above the x-axis, reaching its peak just before \(\pi/4\), crosses the x-axis near \(\pi/2\), reaches a minimum around \(3\pi/2\), and ascends, peaking just before \(2\pi\). ### Graph Analysis: - **Wave Patterns**: - Both curves exhibit typical wave patterns with periodic increases and decreases. - The curves appear out of phase, with peaks and troughs occurring at different x-values. - **Intersection Points**: - The curves intersect in intervals, notably around \(x = 0\) and \(x = \pi\). These sinusoidal graphs can represent various wave-related phenomena such as sound waves, light waves, or alternating current in electrical circuits. Their properties, such as frequency and amplitude, can be analyzed from their periodicity and height.
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