For the function $f(x)=-3 \sin \left(x-\frac{\pi}{4}\right)$, determine its amplitude and period, and then graph it for two periods.
Enter the exact answers.
For the number $\pi$, either choose $\pi$ from the bar at the top or type in $\mathrm{Pi}$ (with a capital P).
Amplitude: $A=$
Period: $P=$
Using your answers for the amplitude and period, select the correct graph of the function $f(x)=-3 \sin \left(x-\frac{\pi}{4}\right)$
Answer
\(\boxed{\text{Amplitude: } A=3, \text{ Period: } P=2\pi}\)
Step 1 ：Given the function $f(x)=-3 \sin \left(x-\frac{\pi}{4}\right)$, we can compare it to the general form of a sine function, which is $f(x) = A \sin(Bx + C)$.
Step 2 ：In this case, we have $A = -3$ and $B = 1$.
Step 3 ：The amplitude is the absolute value of $A$, so the amplitude is $A=|(-3)|=3$.
Step 4 ：The period is $\frac{2\pi}{|B|}$, so the period is $P=\frac{2\pi}{|1|}=2\pi$.
Step 5 ：\(\boxed{\text{Amplitude: } A=3, \text{ Period: } P=2\pi}\)
