Final answer:
The range of the function f(x) = 2x^2 - 8 with the domain (-2,0] U {2} is [-8, 8].
Step-by-step explanation:
To find the range of the function f given its domain, we first need to understand the nature of the function. In this case, f(x) = 2x2 - 8 is a quadratic function, and its graph is a parabola opening upwards since the coefficient of x2 is positive.
Looking at the domain (-2, 0] U {2}, we see that it consists of two intervals: all numbers between -2 and 0 (including 0) and the number 2. The value of the function at x = 0 is f(0) = -8, and since the parabola is opening upwards, this will be the minimum value of the function within that interval. At x = 2, the function value is f(2) = 2(2)2 - 8 = 8. Since this is the only point outside the interval (-2, 0], it will be the maximum value of the function in the provided domain.
Therefore, the range of the function within the given domain is [-8, 8].