Question

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

Answer 1

See graph and explanation.

Explanation:

Upon changing x to `-x` in f ( x), it becomes `f ( - x )`,

If f( - x ) = - f ( x ), the graph changes as mirror image with respect

to x-axis and the function is an odd function. Here, the combined

graph of both is symmetrical about x-axis. Example: sin x.

See separate graphs..

Graph of `y = sin ( -x ) = - sin x`:
graph{y + sin x = 0}
Graph of `y = sin x`::
graph{y - sin x = 0}
Combined graph of `y = sin ( -x )` and y = sin x::
graph{y^2 - (sin x)^2 = 0}

If f( - x ) = f ( x ), the graph does not change and the function i an

even function. Example `cos ( - x ) = cos x`. Here the graph is

symmetrical about y-axis.