For the function y=-3 + cos (x + 4) ], what is the minimum value?

-4 is the mimumum of y=-3+cos (x+4)

Step-by-step explanation:

The minimum value of y=cos (x) is - 1.

The minimum value of y=cos (x+4) is still - 1; the + 4 inside the cosine function only affected the horizontal shift.

The minimum value of y=-3+cos (x+4) is - 3-1 which is - 4. This brought the graph down 3 units so if the minimum was previously - 1 and it got brought down 3 units then it's new minimum is - 4.