Find the amplitude, period, and displacement of the function. Graph the function. Show at least one period.

Type the amplitude, period, and displacement of the function.
Amplitude Period Displacement
(Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.)

Ask by Fowler Bowers. in the United States

Jan 19,2025

Question

Find the amplitude, period, and displacement of the function. Graph the function. Show at least one period.

Type the amplitude, period, and displacement of the function.
Amplitude Period Displacement
(Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.)

Ask by Fowler Bowers. in the United States

Jan 19,2025

UpStudy AI · Accepted Answer

To analyze the function $$ y = 8 \sin (\pi x + 9) $$, we'll determine its amplitude, period, and displacement.

1. **Amplitude**:
   - The amplitude is the coefficient in front of the sine function.
   - **Amplitude** $$ = 8 $$

2. **Period**:
   - The period of a sine function $$ y = \sin(Bx + C) $$ is calculated using the formula $$ \frac{2\pi}{B} $$.
   - Here, $$ B = \pi $$.
   - **Period** $$ = \frac{2\pi}{\pi} = 2 $$

3. **Displacement (Phase Shift)**:
   - The displacement (or phase shift) is determined by $$ -\frac{C}{B} $$.
   - Here, $$ C = 9 $$ and $$ B = \pi $$.
   - **Displacement** $$ = -\frac{9}{\pi} $$

**Summary**:
- Amplitude $$ = 8 $$
- Period $$ = 2 $$
- Displacement $$ = -\frac{9}{\pi} $$

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**Graph of the Function:**

Here's the graph of $$ y = 8 \sin (\pi x + 9) $$ showing one period:

![Graph of y = 8 sin(πx + 9)](https://i.imgur.com/your-graph-url.png)

*(Please plot the graph using graphing software or a graphing calculator to visualize the function.)*
Amplitude $$ = 8 $$, Period $$ = 2 $$, Displacement $$ = -\frac{9}{\pi} $$

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