Question

Given f(x)= sin x, g(x)= cos 2x, how do you graph h(x)= (f-g)(x)?

Answer 1

The best way is to use technology. The graph is fairly interesting because of the different frequencies involved in the difference of these functions.

Explanation:

Here is the graph:

graph{sin(x)-cos(2x) [-5, 5, -2.5, 2.5]}

You might want to also see if you can understand why the graph looks this way by plotting `f` and `g` individually and looking at the "signed distance" between them (vertically-speaking, for each fixed value of `x`).