For this case we have the following definitions:
A function is even if, for each x in the domain of f, f (- x) = f (x). The even functions have reflective symmetry through the y-axis.
A function is odd if, for each x in the domain of f, f (- x) = - f (x). The odd functions have rotational symmetry of 180º with respect to the origin.
We then have the following function:
\(f (x) = 9 - 4x ^ 2
\)
Applying the definitions we have:
\(f (-x) = 9 - 4 (-x) ^ 2
f (-x) = 9 - 4 (x) ^ 2
f (-x) = f (x)
\)
Answer:
The function is not odd because it is fulfilled:
\(f (-x) = f (x)
\)
Therefore, the function is even.
