Question

How do you graph `y=-cosx`?

Answer 1

The graph of `y=-cos(x)` is below:
graph{-cos(x) [-6, 6, -2, 2]}
See the explanation.

Explanation:

Start from `y=cos(x)`:
graph{cos(x) [-6, 6, -2, 2]}

For the same value of argument `x` function `-cos(x)` takes a value that is equal to the value of `cos(x)` by absolute value, but opposite in sign.

So, whenever `cos(x)` is positive, `-cos(x)` is symmetrically negative with the X-axis being an axis of symmetry.
And, whenever `cos(x)` is negative, `-cos(x)` is symmetrically positive with the X-axis being an exis of symmetry.

The graph of `y=-cos(x)` is below:
graph{-cos(x) [-6, 6, -2, 2]}
As you see, it's mirror image of a graph of function `y=cos(x)` with the X-axis acting as a mirror..

In general, graphs of `y=f(x)` and `y=-f(x)` are symmetrical relative to the X-axis.