Based on the given cubic function f(x) = 2x(x - 3)(x + 5), the roots of the function or what make f(x) = 0 is when x = 0, x = 3, and x = -5.
In terms of end behavior, since the highest degree (3) is an odd number and the leading coefficient (2) is a positive number, the end behavior is:
If x approaches positive infinity, the y-values approaches positive infinity as well.
If x approaches negative infinity, the y-values approaches negative infinity too.
Here is the sketch of the cubic function showing its roots and its end behavior.
As you can see in the graph above, there are three points located on the x-axis. We have (-5, 0), (0,0), and (3,0). These are the roots of the function.