What does the graph of y = cos(x) + 3 look like?

Like any other function, when we add or subtract a number at the end of the equation, it will either move the equation up (if it's positive) or move it down (if it's negative).  We have a +3, so the parent cos function moves up 3.  It oscillates between y values of 4 and 2 and 3 is its midline.  So, in summary, the new function looks exactly like the parent, same size and shape and orientation, it's just shifted up 3 units.