# Question #f6ba4

Oct 18, 2017

it's EVEN if f(-x) = f(x) for all x in the domain

#### Explanation:

...because one definition of an even function is that its graph is symmetrical about the y axis.

If you can fold the graph along the y axis, and lay the right side of the paper over the left, and the graph superimposes on itself, it's an even function.

Some examples:

$y = {x}^{2}$ is EVEN, while $y = {x}^{3}$ is ODD.

$y = \cos \left(x\right)$ is EVEN, while $y = \sin \left(x\right)$ is ODD.

GOOD LUCK

Update: the definition is only complete if you add:

a function is ODD if f(-x) = -f(x) for all x in the domain.

So, $y = {x}^{3}$ is odd by that definition, and $y = {e}^{x}$ is NEITHER.

GOOD LUCK

Oct 18, 2017

An even function has the same y value for a given x and -x
An odd function has a y value for a given x and a -y value for -x. Otherwise, the graph is neither.

#### Explanation:

Here is a graph of an even function.

graph{cos(x) [-10, 10, -5, 5]}

Please observe that it has the same y value for $x = 1$ and $x = - 1$.

Here is a graph of an odd function:

graph{sin(x) [-10, 10, -5, 5]}

Please observe that y value corresponding to $x = 1$ and observe that is has same y value but negative for $x = - 1$.

Here is a graph of a function that is neither.

graph{e^x [-10, 10, -5, 5]}