Find the period and amplitude of the function.=y−3sinπxGive the exact values, not decimal approximations.

1. Break Down the Problem

We need to determine the period and amplitude of the function given by $y = -3\sin(\pi x)$.

2. Relevant Concepts

• Amplitude of a sine function $y = a\sin(bx)$ is given by the absolute value of $a$, i.e., $|a|$.
• Period of the sine function is calculated using the formula $\frac{2\pi}{b}$, where $b$ is the coefficient of $x$ in the sine function.

3. Analysis and Detail

From the function $y = -3\sin(\pi x)$:

• Here, $a = -3$ and $b = \pi$.

Amplitude Calculation: $\text{Amplitude} = |a| = |-3| = 3$

Period Calculation: $\text{Period} = \frac{2\pi}{b} = \frac{2\pi}{\pi} = 2$

4. Verify and Summarize

The amplitude has been determined to be $3$, and the period has been verified to be $2$.

Final Answer

• Amplitude: $3$
• Period: $2$