Answer
See the image below.
Work Step by Step
To graph the function, first we will determine its parent function and then apply the transformations to sketch it.
The parent function for $y=\frac{1}{4}tan(x-\frac{\pi}{4})$ is $y=tanx$ (Black dotted line on the image).
Now let's apply a transformation: $y=tan(x-\frac{\pi}{4})$, which means that we shift the parent graph to the right by $\frac{\pi}{4}$ unit (Red line graph on the image).
Finally, let's apply the last transformation: $y=\frac{1}{4}tan(x-\frac{\pi}{4})$, which means shrinking the graph vertically by a factor of 4 (Green line graph on the image).
