#### Answer

one-to-one

#### Work Step by Step

The graph of $y=\displaystyle \frac{4}{x-8}$ is obtained from the graph of $f(x)=\displaystyle \frac{1}{x}$
by shifting it right by 8 units, $f(x-8)$
and vertically stretching it by factor 4, $...4f(x-8)$.
This graph passes the Horizontal Line Test, so the function is one-to-one