Question

How do you determine if `y=-x^3` is an even or odd function?

Answer 1

y is odd.

Explanation:

y(x) is even or odd according as `y(-x)=+-y(x)`.
Here, #y(-x)=-(-x)^3=-(-x^3)=x^3=-y(x).
So, y is an odd function of x.

The graph of an odd function will be symmetrical about the origin.
If (x, y) is a point on the graph. its mirror image with respect to the origin (# -x, -y) will be on the graph.