Question

How to determine whether the given function is even,odd, or neither?f(x) = x^3 + x^2 + 3

Answer 1

f(x) = x^3 + x^2 + 3x^0 is neither even nor odd.  Why?  Because we have a mixture of even and odd powers of x here:  x^3 (odd) and x^2 and x^0 (even).

Even functions:  all component functions are even (e. g., x^2 and x^0).

Odd functions:  all component functions are odd (e. g., x^5 and x^3.

Neither:              There's a mixture of even ad odd functions.

Another way to test for even, odd or neither:

Even functions:  f(-x) = f(x).  Changing the sign of the input (x) doesn't change the sign of the output.

Odd functions:  f(-x) = -f(x).  Changing the sign of the input changes the sign of the output.