Answer
For the graph see the image below.
The function is not a one-to-one function.
Work Step by Step
$f(x)=|x|-|x-6|$, we can sketch the graph for the following function using a graphing calculator (See the image above).
As we can clearly see from the graph it is not a one-to-one function, since there is a $y$ value of the graph which corresponds to more than one $x$ value.
