Question

How do you graph `y=(cos2x)/2`?

Answer 1

Start with `y=cos(x)`
graph{cos(x) [-7, 7, -1.5, 1.5]}
Next, to change the argument from `x` to `2x`, we should "squeeze" the graph horizontally by a factor of 2 because, if a point `(a,b)` belongs to a graph of a function `y=f(x)`, a point `(a/2,b)` belongs to a graph of `y=f(2x)`.
graph{cos(2x) [-7, 7, -1.5, 1.5]}
Finally, we have to "squeeze" the graph vertically by a factor of 2 because, if a point `(a,b)` belongs to a graph of `y=f(x)`, a point `(a,b/2)` belongs to a graph of `y=f(x)/2`:
graph{cos(2x)/2 [-7, 7, -1.5, 1.5]}