Question

How do you graph `y= -sin(2x)-1/2`?

Answer 1

Analyze the function and draw incremental graphs of the function.

Explanation:

1. Trace a sin(x) on the paper.
2. Double the frequency of the sin, so that the function y=sin(2x) pass through the points `(0,0), (pi/4,1), (pi,0), (3/4pi,-1) ...`
3. Reflect the positive with the negative part (as if the x-axis were a mirror)
4. Translate down of 1/2. As if the function fell down of half step.

graph{-sin(2x)-1/2 [-10, 10, -5, 5]}