Determine whether the function, f = 1 + x + x^2, is odd, even, or neither.
A function is even when f(x) = f(-x)
Since f(x) = 1 + x + x^2 and f(-x) = 1 - x + x^2, then f(x) ≠ f(-x)
The function is not even.
A function is odd when –f(x) = f(-x)
Since f(x) = 1 + x + x^2, giving –f(x) = -1 – x – x^2, and f(-x) = 1 - x + x^2, then -f(x) ≠ f(x)
The function is not odd.
Conclusion: The function is neither odd nor even