Here is a graph of x^3
The negative regions of a function are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero)
So here, the value that is below the x axis is x< 0 , as you can see from the left side of the graph, the curve is under the x axis. Also, notice that it started to go down the x axis at the point where the value of x is less than zero. To visualize it more clearly, look at x = -1. At that point, the graph of x^3 is below the x axis . And also in -2, -3 and so on.
Another way to look at it is by substituting these negative values of x in the parent function f(x)= x^3. Example , if x = -1, then f(x) = (-1)^3 + -1; if x = -2, then f(x) = (-2)^3 = -8 and so on. Meaning all the negative values of x will yield a negative value of f (x). Thus, interval to which the function f(x)=x^3 is negative is when x<0 (but not including zero, since the cube of zero is also zero, it's not a negative value)
