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

##### 1 Answer
Jul 19, 2018

See graph and explanation.

#### Explanation:

Upon changing x to $- x$ in f ( x), it becomes $f \left(- x\right)$,

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 $y = \sin \left(- x\right) = - \sin x$:
graph{y + sin x = 0}
Graph of $y = \sin x$::
graph{y - sin x = 0}
Combined graph of $y = \sin \left(- x\right)$ 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 $\cos \left(- x\right) = \cos x$. Here the graph is

symmetrical about y-axis.