Final answer:
The function f(x)=5x^2 is an even function because f(-x) equals f(x) and does not satisfy the criteria for an odd function, as -f(x) does not equal f(-x).
Step-by-step explanation:
To determine whether the function f(x)=5x^2 is even, odd, or neither, we need to evaluate f(-x) and -f(x).
Firstly, let's find f(-x):
f(-x) = 5(-x)^2 = 5x^2 = f(x)
This shows that f(x) is equal to f(-x), which is the property of an even function. An even function is symmetric about the y-axis.
Now let's find -f(x):
-f(x) = -5x^2
However, if f(x) were an odd function then we would have -f(x) = f(-x). Since -f(x) does not equal f(-x) in this case, f(x) is not an odd function.
Since f(x) matches the criteria for an even function and not an odd function, we can conclude that f(x)=5x^2 is an even function.