I assume the question is about the range of a function f.
First, determine the domain of the function f. This is the set of all inputs. Use this information to find all the output values of f: that is the range. In most cases, you will not have to evaluate f for each and every input: the nature of f will help you.
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The domain of x^3 - 2x is whatever you choose it to be. That will then determine the range.
P = f/a
If you can differentiate the function, then you can tell that the graph is concave down if the second derivative is negative over the range examined. As an example: for f(x) = -x2, f'(x) = -2x and f"(x) = -2 < 0, so the function will be everywhere concave down.
Take the largest number minus the smallest number to determine the range.
The "maximum" function.