Answer
One-to-one.
Work Step by Step
A function is one-to-one if different inputs have different function values.
Algebraically written, $x_{1}\neq x_{2}\Rightarrow f(x_{1})\neq f(x_{2})$
This is logically equivalent to
If $f(x_{1})=f(x_{2})$, then $x_{1}=x_{2}\qquad $(contraposition.)
So, let us assume that $f(x_{1})=f(x_{2})$.
Then
$-x_{1}=x_{2}\qquad$... multiply with (-1)
$x_{1}=x_{2}$
So, from $f(x_{1})=f(x_{2})$, it follows that $x_{1}=x_{2}$,
which means that no two x's have the same function value,
which means that the function is one-to-one.
NOTE:
A graphical approach is to graph the function and see if it passes the horizontal line test.
The graph of this function is an oblique line and passes the test.
(No horizontal line cuts the graph in more than one point.)
