1. The problem asks for the phase shift of the function $$y = 4 \cos(x + \pi) - 2$$. 2. The general form of a cosine function with phase shift is $$y = A \cos(B(x - C)) + D$$, where: - $A$ is the amplitude, - $B$ affects the period, - $C$ is the phase shift, - $D$ is the vertical shift. 3. To find the phase shift, we focus on the inside of the cosine: $$x + \pi$$. 4. Rewrite $$x + \pi$$ as $$x - (-\pi)$$ to match the form $$x - C$$. 5. Therefore, the phase shift is $$C = -\pi$$. 6. A negative phase shift means the graph shifts to the left by $$\pi$$ units. 7. The vertical shift is $$-2$$, which moves the graph down 2 units, but this does not affect the phase shift. Final answer: The phase shift is left $$\pi$$ units.