Given the following function

graph the three functions y = f(x), y = f(-x), and y = -f(-x) and see if any two of the graphs coincide.

Using Maple:

> f:= x -> sin(x)+4*x^3;

> plot({f(x),f(-x)}, x=-1..1);

> plot({f(x),-f(-x)}, x=-1..1);

It appears from the latter graph that the two functions y = f(x) and y = -f(-x) are the same. Hence, it appears that the function y = f(x) is odd.