TITLE: Even, Odd, or Neither
QUESTION [5 upvotes]: I would like someone to verify my solutions to the problems above?
9a. even 
9b. odd
10. neither

REPLY [5 votes]: Yes, you are right.
Proper explanation
We say function $f$ is even, if for each $x \in D_1$, where $D_1$ is the domain of the function $f$, the following condition is satisfied:
$$
f(x) = f(-x).
$$
On the other hand, we say, that function $g$ is odd, if for each $x \in D_2$, where $D_2$ is the domain of the function $g$, the following condition is satisfied:
$$
- g(x) = g(-x)
$$
That's exactly the same as the fact, that $f$ is symmetric about the $y$-axis, resp. that $g$ is symmetric about the origin point in the coordinate system (simply the point $[0,0]$).
But usually I assume you won't be given the graph of the function, or you would not be able to draw the graph of the function precisely.
One of the easiest examples are:
even function $f(x) = \vert\, x\,\vert $, where $|\cdot|$ is absolute value.
odd function $g(x) = x $.
Task.
Of course not every function is even or odd, but there is one function which is both even and odd. Try to find it!