Question

How do you graph `y=6cosx`?

Answer 1

See below:

Explanation:

We can start with the graph of `y=cosx`:

graph{cosx [-6.25, 6.25, -8, 8]}

The graph runs `-2pi<=x<=2pi`. Max `y = 1` at `x=0, -2pi, 2pi`; Min `y = -1` at `x=-pi, pi`. And the x-intersects are at `x=pi/2, (3pi)/2, -pi/2, -(3pi)/2`.

So how does the graph change? The equation `y=6cosx` will increase the y result for any x by 6 - so in essence we're just moving the Max y and Min y marks from 1 and -1 to 6 and -6. That looks like this:

graph{6cosx [-6.25, 6.25, -8, 8]}