Determine whether each function below is an even function, an odd function, or neither.

1. $f(x) = x^2$

   Hint (a):

   Definition of an even function: $f(a) = f(−a)$.
   Definition of an odd function: $f(−a) = −f(a)$.

   Steps (a):

   $f(x) = x^2$
   $f(a) = (a)^2 = a^2$
   $f(−a) = (−a)^2 = a^2$.......... $f(a) = f(−a)$ it's even!
   $−f(a) = −(a)^2 = −a^2$.............$f(−a) \ne −f(a)$ it's NOT odd.

2. $f(x) = x^3$

   Hint (b):

   Refer to hint and steps in part (a).

3. $f(x) = 2^x$

   Hint (c):

   Refer to hint and steps in part (a).

4. $f(x) = \sin(x)$

   Hint (d):

   Even functions are symmetrical over the $y$-axis.
   Odd functions are symmetrical about the origin.

   Hint (d):

   Sketch a graph of $\sin x$ and describe the symmetry.