15) y = 2 cos(-3x - π/3) a) π/3 units to the right b) π/3 units to the left c) π/9 units to the right d) π/9…

Explanation:

Step1: Rewrite the cosine - function in standard form

The general form of a cosine function is $y = A\cos(Bx - C)+D$. Given $y = 2\cos(-3x-\frac{\pi}{3})$, we can rewrite it as $y = 2\cos\left[-(3x+\frac{\pi}{3})\right]=2\cos\left(3x + \frac{\pi}{3}\right)$ (since $\cos(-\theta)=\cos(\theta)$). For a cosine function $y = A\cos(Bx - C)+D$, the phase - shift is given by $\frac{C}{B}$. Here, $B = 3$ and $C=-\frac{\pi}{3}$.

Step2: Calculate the phase - shift

The formula for the phase - shift of the cosine function $y = A\cos(Bx - C)+D$ is $\text{Phase - shift}=\frac{C}{B}$. Substituting $B = 3$ and $C =-\frac{\pi}{3}$ into the formula, we get $\text{Phase - shift}=\frac{-\frac{\pi}{3}}{3}=-\frac{\pi}{9}$. A negative phase - shift means a shift to the left.

Answer:

D. $\frac{\pi}{9}$ units to the left