Answer
The red graph is the result.
Domain: $(-\infty,0)\cup(0,\infty)$
Range: $(-\infty,2)\cup(2,\infty)$
Work Step by Step
$h(x)=\displaystyle \frac{4}{x}+2=4\left(\frac{1}{x}\right)+2$
Starting with the graph of $y=\displaystyle \frac{1}{x}$
1. Stretch vertically by a factor of 4 to obtain ... $y=\displaystyle \frac{4}{x}$
2. vertically shift upward 2 units to obtain .... $y=\displaystyle \frac{4}{x}+2$
Plot several points of $\displaystyle \frac{1}{x},$
perform the transformations 1-2 on each,
and join (red on the image).
Reading from the graph,
Domain: $(-\infty,0)\cup(0,\infty)$
Range: $(-\infty,2)\cup(2,\infty)$
