Determine the amplitude, period, and phase shift (if any) of the given function. Graph the function. $$ y=\sin x+7 $$ What is the amplitude of $$ y=\sin x+7 $$ ? (Simplify your answer. Type an exact answer, using $$ \pi $$ as needed.)

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To analyze the function $$ y = \sin x + 7 $$, we can identify the amplitude, period, and phase shift.

1. **Amplitude**: The amplitude of a sine function $$ y = A \sin(Bx + C) + D $$ is given by the absolute value of $$ A $$. In this case, the function can be rewritten as:
   $$
   y = 1 \cdot \sin(x) + 7
   $$
   Here, $$ A = 1 $$. Therefore, the amplitude is:
   $$
   \text{Amplitude} = |A| = |1| = 1
   $$

2. **Period**: The period of a sine function is given by the formula $$ \frac{2\pi}{|B|} $$. In this case, $$ B = 1 $$ (since there is no coefficient in front of $$ x $$). Thus, the period is:
   $$
   \text{Period} = \frac{2\pi}{|1|} = 2\pi
   $$

3. **Phase Shift**: The phase shift is determined by the term $$ C $$ in the function $$ y = A \sin(Bx + C) + D $$. In this case, there is no horizontal shift since there is no $$ C $$ term. Therefore, the phase shift is:
   $$
   \text{Phase Shift} = 0
   $$

4. **Vertical Shift**: The function $$ y = \sin x + 7 $$ has a vertical shift of 7 units upward.

### Summary:
- **Amplitude**: $$ 1 $$
- **Period**: $$ 2\pi $$
- **Phase Shift**: $$ 0 $$

### Graphing the Function:
To graph $$ y = \sin x + 7 $$:
- The sine function oscillates between -1 and 1. Therefore, $$ \sin x $$ oscillates between -1 and 1, and when we add 7, the function $$ y = \sin x + 7 $$ oscillates between $$ 6 $$ and $$ 8 $$.
- The midline of the graph is at $$ y = 7 $$.
- The graph will have peaks at $$ y = 8 $$ and troughs at $$ y = 6 $$.

You can sketch the graph by plotting points for key angles (like $$ 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi $$) and noting the vertical shift. The graph will repeat every $$ 2\pi $$ units.
Amplitude: 1, Period: $$ 2\pi $$, Phase Shift: 0

Determine the amplitude, period, and phase shift (if any) of the given function. Graph the function. \( y=\sin x+7 \) What is the amplitude of \( y=\sin x+7 \) ? (Simplify your answer. Type an exact answer, using \( \pi \) as needed.)

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