Determine whether the function f(x) = x^3 - 3x is odd, even, or neither.

Step 1 ：First, we need to know the definitions of even and odd functions. A function f(x) is even if f(-x) = f(x) for all x in the function's domain, and it's odd if f(-x) = -f(x) for all x in the function's domain.

Step 2 ：To check whether the function is even, we substitute -x for x in the equation: f(-x) = (-x)^3 - 3(-x) = -x^3 + 3x

Step 3 ：We can see that f(-x) is not equal to f(x), so the function is not even.

Step 4 ：Next, to check whether the function is odd, we see if f(-x) is equal to -f(x). If we multiply the original function by -1, we get -f(x) = -(x^3 - 3x) = -x^3 + 3x

Step 5 ：We can see that f(-x) is equal to -f(x), so the function is odd.