I know It's probably an easy question but I don't know remember how to do it.
Show the work to determine if the relation is even, odd, or neither.
a ) f(x) = 2x^2 - 7
b) f(x) = -4x^3 - 2x
c) f(x) = 4x^2 - 4x + 4
If f(-x) = f(x), for any x, the function is even.
If f(-x) = -f(x), for any x, the function is odd.
It can be neither.
Try substituting -x for x and see what you get.
Hint: Two of the functions are neither even nor odd.
Only c) is neither even nor odd.
To determine if a relation is even, odd, or neither, we need to evaluate the function for both f(-x) and f(x).
For a), the function is f(x) = 2x^2 - 7.
To check if it is even, we substitute -x for x and see if we get the same result.
f(-x) = 2(-x)^2 - 7
= 2x^2 - 7
Since f(-x) is equal to f(x), the function is even.
For b), the function is f(x) = -4x^3 - 2x.
Again, we substitute -x for x and check if we get the same result.
f(-x) = -4(-x)^3 - 2(-x)
= -4x^3 + 2x
Since f(-x) is NOT equal to f(x), but rather the negative of f(x), the function is odd.
Finally, for c), the function is f(x) = 4x^2 - 4x + 4.
We substitute -x for x and check the result.
f(-x) = 4(-x)^2 - 4(-x) + 4
= 4x^2 + 4x + 4
Since f(-x) is NOT equal to f(x) nor the negative of f(x), the function is neither even nor odd.
Therefore, a) is even, b) is odd, and c) is neither even nor odd.