Question

How do you graph `y=4cos(1/2x)`?

Answer 1

Sketch the graph of `y=cos x` then stretch by a factor 2 in the `x`-direction and a factor 4 in the `y`-direction.

Explanation:

The `1/2` inside the cosine function causes a stretch of factor 2 in the `x`-direction and the 4 multiplying the cosine causes a stretch of factor 4 in the `y`-direction.
graph{y=cosx [-4.07, 8.414, -3.6, 2.64]}
graph{y=cos(x/2) [-4.07, 8.414, -3.6, 2.64]}
graph{y=4cos(x/2) [-4.07, 8.414, -3.6, 2.64]}