Let
$f(x) = \left(x+\frac{1}{x}\right)$

Then the given function g is given by

$g(x) = \frac{1}{3} f(x)$

Therefore, $c = 1/3$, and the graph of $g$ is obtained from that of the function $f$ by compressing it by a factor of $1/c = 3$ in the $y$-direction.