what the answer for this/how is my answer wrong ### Transcription of Content for Educational Use**Objective:**Graph the following function over a one-period interval.**Function:**\[ y = -2\cos\left(x + \frac{\pi}{8}\right) \]**Instructions:**Use the graphing tool to graph the equation. Type "pi" to insert $ \pi $ as needed.**Graph Description:**- The graph displayed is of the function $ y = -2\cos\left(x + \frac{\pi}{8}\right) $.- It is a cosine wave reflecting over the x-axis due to the negative sign in front of the 2.- The amplitude (the peak value from the centerline) is 2.- The period of one complete cycle is $ 2\pi $.- There is a horizontal shift to the left by $ \frac{\pi}{8} $.- The vertical shift is 0, so the midline of the function is along the x-axis.- The graph oscillates between -2 and 2 on the y-axis.**Graphing Tool Settings:**- Amplitude: 2- Period: $ 2\pi $- Vertical Shift: 0- Horizontal Shift: $ -\frac{\pi}{8} $- Reflection: Reflect over x-axis is selected.### Diagram Explanation:The diagram shows a trigonometric graph where the curve starts from an initial phase shift by $ \frac{\pi}{8} $, continues through its maximum and minimum points, and completes one full cycle of $ 2\pi $. The cosine wave is inverted due to the negative sign, maintaining the characteristic sine wave shape but reflected vertically.For further analysis and interactive graphing, please refer to the graphing tool provided.

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Description: what the answer for this/how is my answer wrong ### Transcription of Content for Educational Use**Objective:**Graph the following function over a one-period interval.**Function:**\[ y = -2\cos\left(x + \frac{\pi}{8}\right) \]**Instructions:**Use the

Answered: Graph the following function over a…

Math

Calculus

Graph the following function over a one-period interval. y= - 2cos x+ 8

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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what the answer for this/how is my answer wrong

### Transcription of Content for Educational Use

**Objective:**
Graph the following function over a one-period interval.

**Function:**
\[ y = -2\cos\left(x + \frac{\pi}{8}\right) \]

**Instructions:**
Use the graphing tool to graph the equation. Type "pi" to insert $ \pi $ as needed.

**Graph Description:**
- The graph displayed is of the function $ y = -2\cos\left(x + \frac{\pi}{8}\right) $.
- It is a cosine wave reflecting over the x-axis due to the negative sign in front of the 2.
- The amplitude (the peak value from the centerline) is 2.
- The period of one complete cycle is $ 2\pi $.
- There is a horizontal shift to the left by $ \frac{\pi}{8} $.
- The vertical shift is 0, so the midline of the function is along the x-axis.
- The graph oscillates between -2 and 2 on the y-axis.

**Graphing Tool Settings:**
- Amplitude: 2
- Period: $ 2\pi $
- Vertical Shift: 0
- Horizontal Shift: $ -\frac{\pi}{8} $
- Reflection: Reflect over x-axis is selected.

### Diagram Explanation:

The diagram shows a trigonometric graph where the curve starts from an initial phase shift by $ \frac{\pi}{8} $, continues through its maximum and minimum points, and completes one full cycle of $ 2\pi $. The cosine wave is inverted due to the negative sign, maintaining the characteristic sine wave shape but reflected vertically.

For further analysis and interactive graphing, please refer to the graphing tool provided.

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