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
Final Answer: The correct graph of the function \(f(x)=-3 \sin \left(x-\frac{\pi}{4}\right)\) has an amplitude of 3, a period of \(2\pi\), a phase shift of \(\frac{\pi}{4}\), and no vertical shift.
Step 1 ：Given the function: \(f(x) = -3 \sin \left(x - \frac{\pi}{4}\right)\)
Step 2 ：Identify the general form: \(f(x) = A \sin(B(x - C)) + D\)
Step 3 ：Find the amplitude: \(|A| = |-3| = \boxed{3}\)
Step 4 ：Find the period: \(\frac{2\pi}{|B|} = \frac{2\pi}{1} = \boxed{2\pi}\)
Step 5 ：Find the phase shift: \(C = \boxed{\frac{\pi}{4}}\)
Step 6 ：Find the vertical shift: \(D = \boxed{0}\)
Step 7 ：Final Answer: The correct graph of the function \(f(x)=-3 \sin \left(x-\frac{\pi}{4}\right)\) has an amplitude of 3, a period of \(2\pi\), a phase shift of \(\frac{\pi}{4}\), and no vertical shift.
