identify the values for the function $y = \\cos 4(x - \\pi)$. amplitude = period = horizontal (phase) shift…

Explanation:

Step1: Recall amplitude formula

For $y = A\cos(B(x - C))+D$, amplitude is $|A|$. Here $A = 1$, so amplitude $=|1| = 1$.

Step2: Recall period formula

The period of $y=\cos(B(x - C))+D$ is $T=\frac{2\pi}{|B|}$. Given $B = 4$, then $T=\frac{2\pi}{4}=\frac{\pi}{2}$.

Step3: Recall phase - shift formula

The horizontal (phase) shift of $y=\cos(B(x - C))+D$ is $C$. Here $C=\pi$, so the horizontal (phase) shift is $\pi$ units.

Step4: Recall vertical - shift formula

For $y=\cos(B(x - C))+D$, the vertical shift is $D$. Here $D = 0$, so the vertical shift is $0$ units.

Answer:

Amplitude = 1 Period = $\frac{\pi}{2}$ Horizontal (phase) shift = $\pi$ units Vertical shift = 0 units