Question

How do you graph `y = -sin(2x)`?

Answer 1

These are three steps (transformations) that you can apply in every order you want,and you'll obtain `y=-sin(2x)`.

Explanation:

1. Start graphing the trig function you know, `y=sin(x)`.

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

1. Doubling the argument you have a compression in the period, that means that the function double the frequency: if we had the solutions in `0,pi,2pi,3pi,...` now we have solutions in `0,pi/2,pi,3/2pi,2pi,...`

graph{sin(2x) [-10, 10, -5, 5]}

1. The minus sign in front of the function is a reflection on the x-axis, so for each point of the function `(x,y)->(x,-y)`:

graph{-sin(2x) [-10, 10, -5, 5]}