Question

How do you graph `f(x)= 2 sin 4x`?

Answer 1

A general sine graph of form `y=AsinBx` has amplitude A and period `360^@/B`.

So in this case, `y=2sin4x` has amplitude `2` which is the maximum displacement from the x-axis, and period `T=360^@/4=90^@=(pi)/2 rad` and represents the distance on the x-axis for 1 complete cycle.

So the graph becomes :

graph{2sin(4x) [-4.385, 4.384, -2.19, 2.195]}