### Home > APCALC > Chapter 2 > Lesson 2.1.1 > Problem2-12

2-12.

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

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

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

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

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

Refer to hint and steps in part (a).

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

Refer to hint and steps in part (a).

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

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

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