Answer
See graph and explanations.
Work Step by Step
Step 1. Graph the function $f(x)=\frac{1}{x}$ as shown in the figure with the blue curve.
Step 2. We can identify that the function has asymptotes of $x=0$ and $y=0$.
Step 3. To get the graph of the function $h(x)=\frac{1}{x-1}+3$, shift the original 1 units to the right and then shift the result up 3 units as shown with the red curve.
Step 4. We can see that the final curve has has asymptotes of $x=1$ and $y=3$.
