Determine if the following functions are even or odd:
1) $$f (x) = 1$$
2) $$f (x) = x$$
3) $$f (x) = x^2$$
See development and solution
Development:
1) The function is pair.
2) Let's see that the function is odd:
$$f (x) =-f (-x)$$
$$x = - (-x)$$
3) Let's verify that the function is pair:
$$f (x) = f (-x)$$
$$x^2=(-x)^2=x^2$$
Solution:
1) Even.
2) Odd.
3) Even.