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Find the equation from the graph.

Find the equation from the graph.

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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Find the equation from the graph. 

The image features a graph of a sinusoidal function labeled \( g(t) \). The horizontal axis represents the variable \( t \), with tick marks ranging from \(-10\) to \(9\). The vertical axis appears to range from \(-3\) to \(3\). ### Description of the Graph: - **Function Type:** The graph is of a periodic sinusoidal wave, which suggests it might be represented by a sine or cosine function. - **Amplitude:** The maximum and minimum values on the vertical axis go from \(-3\) to \(3\). This could imply the amplitude is around 3. - **Period:** From inspection, both peaks and troughs suggest that the graph completes one full cycle approximately every 6 to 7 units along the horizontal axis. - **Phase Shift and Vertical Shift:** The graph’s equilibrium does not appear shifted vertically as it oscillates symmetrically around 0, suggesting no vertical shift from the standard position is evident. Any phase shift would need to be deduced from standard positions of sine or cosine waves starting at \((0,0)\) or their peaks/troughs. #### Task Presented: "Find an equation for the graph above." There is a text box beneath the graph for inputting the equation and a "Submit Question" button for submission. This graph is commonly used to teach concepts in trigonometry such as identifying properties of trigonometric functions, including amplitude, period, phase shift, and vertical translation.
Transcribed Image Text:The image features a graph of a sinusoidal function labeled \( g(t) \). The horizontal axis represents the variable \( t \), with tick marks ranging from \(-10\) to \(9\). The vertical axis appears to range from \(-3\) to \(3\). ### Description of the Graph: - **Function Type:** The graph is of a periodic sinusoidal wave, which suggests it might be represented by a sine or cosine function. - **Amplitude:** The maximum and minimum values on the vertical axis go from \(-3\) to \(3\). This could imply the amplitude is around 3. - **Period:** From inspection, both peaks and troughs suggest that the graph completes one full cycle approximately every 6 to 7 units along the horizontal axis. - **Phase Shift and Vertical Shift:** The graph’s equilibrium does not appear shifted vertically as it oscillates symmetrically around 0, suggesting no vertical shift from the standard position is evident. Any phase shift would need to be deduced from standard positions of sine or cosine waves starting at \((0,0)\) or their peaks/troughs. #### Task Presented: "Find an equation for the graph above." There is a text box beneath the graph for inputting the equation and a "Submit Question" button for submission. This graph is commonly used to teach concepts in trigonometry such as identifying properties of trigonometric functions, including amplitude, period, phase shift, and vertical translation.
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