The graph of a cosine function has an amplitude of 3, a vertical shift of 1, and a period of 4. These are the only transformations of the parent function.Use the Sine tool to graph the function.The first point must be on the midline, and the second point must be a maximum or minimum value on the graph closest to the first point. ### Graphing a Transformed Cosine FunctionThe graph of a cosine function has an amplitude of 3, a vertical shift of 1, and a period of 4. These are the only transformations of the parent function.Use the Sine tool to graph the function.The first point must be on the midline, and the second point must be a maximum or minimum value on the graph closest to the first point.**Grid Explanation:**Below is a grid for graphing purposes:- The x-axis ranges from -2 to 8.- The y-axis ranges from -6 to 6.- Each grid square represents one unit.**Graphing Instructions:**1. Identify the midline, which, after the vertical shift of 1, will be at y = 1.2. Place the first point on the midline at x = 0, y = 1.3. Determine the maximum and minimum points based on the amplitude. - The maximum will be at y = 1 + 3 = 4. - The minimum will be at y = 1 - 3 = -2.4. Using the period of 4, determine the spacing of the cosine function. - Since one full period is 4 units, x = 0 to x = 4 will complete one cycle.**Steps to Graph the Function:**1. Place the first point at (0, 1) on the midline.2. Place the second point at (1, -2) (minimum value), at the closest x-value.3. Complete the cosine wave using the identified points and amplitude.Use the above grid and steps to accurately plot the transformed cosine function. Remember to mark critical points and draw a smooth curve through these points to complete the graph.

The graph of a cosine function has an amplitude of , a vertical shift of , and a period of . These…

The graph of a cosine function has an amplitude of 3, a vertical shift of 1, and a period of 4. These are the only transformations of the parent function. Use the Sine tool to graph the function. The first point must be on the midline, and the second point must be a maximum or minimum value on the graph closest to the first point.

The graph of a cosine function has an amplitude of 3, a vertical shift of 1, and a period of 4. These are the only transformations of the parent function. Use the Sine tool to graph the function. The first point must be on the midline, and the second point must be a maximum or minimum value on the graph closest to the first point.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

The graph of a cosine function has an amplitude of 3, a vertical shift of 1, and a period of 4. These are the only transformations of the parent function.

Use the Sine tool to graph the function.

The first point must be on the midline, and the second point must be a maximum or minimum value on the graph closest to the first point.

### Graphing a Transformed Cosine Function

The graph of a cosine function has an amplitude of 3, a vertical shift of 1, and a period of 4. These are the only transformations of the parent function.

Use the Sine tool to graph the function.

The first point must be on the midline, and the second point must be a maximum or minimum value on the graph closest to the first point.

**Grid Explanation:**

Below is a grid for graphing purposes:
- The x-axis ranges from -2 to 8.
- The y-axis ranges from -6 to 6.
- Each grid square represents one unit.

**Graphing Instructions:**
1. Identify the midline, which, after the vertical shift of 1, will be at y = 1.
2. Place the first point on the midline at x = 0, y = 1.
3. Determine the maximum and minimum points based on the amplitude.
- The maximum will be at y = 1 + 3 = 4.
- The minimum will be at y = 1 - 3 = -2.
4. Using the period of 4, determine the spacing of the cosine function.
- Since one full period is 4 units, x = 0 to x = 4 will complete one cycle.

**Steps to Graph the Function:**
1. Place the first point at (0, 1) on the midline.
2. Place the second point at (1, -2) (minimum value), at the closest x-value.
3. Complete the cosine wave using the identified points and amplitude.

Use the above grid and steps to accurately plot the transformed cosine function. Remember to mark critical points and draw a smooth curve through these points to complete the graph.

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