Final answer:
The given function f(x) = (x-2)^2 is an even function.
Step-by-step explanation:
A function is even if f(x) = f(-x) for all values of x in the domain of f. On the other hand, a function is odd if f(x) = -f(-x) for all x in the domain of f. Let's analyze the given function, f(x) = (x-2)^2.
To determine if it's even or odd, we substitute -x for x in the function: f(-x) = ((-x)-2)^2 = (-(x+2))^2 = (x+2)^2.
Comparing f(x) = (x-2)^2 with f(-x) = (x+2)^2, we can see that f(x) = f(-x). This means that the given function is an even function.