Question

How do you graph `y=1/2cosx+3`?

Answer 1

your graph is moved up vertically 3 units and its amplitude is cut in half as compared to the parent function `y=cosx`

Explanation:

Use this standard formula to convert from the parent function `y=cosx`

`y=acos(bx-c)+d`

a = amplitude
b = horizontal stretch
c = horizontal shift
d = vertical shift

your function has a amplitude of `1/2` and a vertical shift of `+3`

`y=cosx` has a amplitude of 1 and no shift:

graph{cosx [-10, 10, -5, 5]}

`y=1/2cosx + 3`

So your graph is moved up vertically 3 units and its amplitude is cut in half:

graph{1/2cosx + 3 [-10, 10, -5, 5]}