Which of the following functions illustrates a change in amplitude? - ☐ **A.** y = - 2 - \cos(x - \pi) - ☐ **B.** y = \tan 2x - ☐ **C.** y = - 2 \cos 6x - ☐ **D.** y = 1 + \sin x
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Answer

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Step 1:
Let's solve this step by step:

Step 2:
: Recall the standard form of a trigonometric function

- Standard sine/cosine function: $$y = A \sin(Bx + C) + D
- Where A affects amplitude - Amplitude is the vertical stretch or compression of the wave

Step 3:
: Analyze each function's amplitude

- D. $$y = 1 + \sin x
- Vertical shift is - 2 - Amplitude is unchanged (still 1) - No amplitude change - Only changes period - Multiplying by - 2 changes amplitude from 1 to 2 - Vertical shift is 1 - Amplitude is unchanged (still 1)

Step 4:
: Identify amplitude change

- The $$-2$$ multiplier stretches the cosine wave vertically
- Only option C shows a change in amplitude

Final Answer

**C. y = - 2 \cos 6x** illustrates a change in amplitude.