Answer
See the image below for the graph.
The function is one-to-one.
Work Step by Step
$f(x)=\frac{x+12}{x-6}$, 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 a one-to-one function, since $y$ value corresponds to only one $x$ value.
(Note, at $x=6$ we have horizontal asymptote so the $y$ value never gets two $x$ value).