Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
For the following exercises, graph one period of each given function. Be sure to clearly label five values on the x-axis and the max and min values on the y-axis. ### a) \( f(x) = 2 \sin \left( x + \frac{\pi}{2} \right) \) - **Amplitude:** ______________ - **Period:** ______________ - **Phase Shift:** ______________ - **Vertical Shift:** ______________ The graph area provided shows a set of axes with horizontal and vertical arrows, indicating space to plot the graph. --- ### b) \( g(x) = 3 \cos \left( x - \frac{\pi}{2} \right) \) - **Amplitude:** ______________ - **Period:** ______________ - **Phase Shift:** ______________ - **Vertical Shift:** ______________ This graph area also depicts a set of axes with horizontal and vertical arrows, ready for graphing the function. --- ### c) \( h(x) = \sin \left( x + \frac{\pi}{4} \right) + 1 \) - **Amplitude:** ______________ - **Period:** ______________ - **Phase Shift:** ______________ - **Vertical Shift:** ______________ Another set of axes is presented here with horizontal and vertical arrows for plotting the function. Each set of axes is intended for students to graph one period of the provided trigonometric functions, paying attention to the transformations depicted by amplitude, period, phase shift, and vertical shift.
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Transcribed Image Text:For the following exercises, graph one period of each given function. Be sure to clearly label five values on the x-axis and the max and min values on the y-axis. ### a) \( f(x) = 2 \sin \left( x + \frac{\pi}{2} \right) \) - **Amplitude:** ______________ - **Period:** ______________ - **Phase Shift:** ______________ - **Vertical Shift:** ______________ The graph area provided shows a set of axes with horizontal and vertical arrows, indicating space to plot the graph. --- ### b) \( g(x) = 3 \cos \left( x - \frac{\pi}{2} \right) \) - **Amplitude:** ______________ - **Period:** ______________ - **Phase Shift:** ______________ - **Vertical Shift:** ______________ This graph area also depicts a set of axes with horizontal and vertical arrows, ready for graphing the function. --- ### c) \( h(x) = \sin \left( x + \frac{\pi}{4} \right) + 1 \) - **Amplitude:** ______________ - **Period:** ______________ - **Phase Shift:** ______________ - **Vertical Shift:** ______________ Another set of axes is presented here with horizontal and vertical arrows for plotting the function. Each set of axes is intended for students to graph one period of the provided trigonometric functions, paying attention to the transformations depicted by amplitude, period, phase shift, and vertical shift.
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