GDC Challenge

Who can get closest to producing this graph on their Graphic Display Calculator?

You wouldn't be expected to get this graph exactly. The challenge is to get as close as possible.

Here are some clues:

1. It's an algebraic fraction;
   
   
2. It has three roots. They are \( 0 \; \text{and} \; \pm \sqrt 2 \);
   
   
3. There are vertical asymptotes at \( x = \pm \sqrt 5\);
   
   
4. \( y = \frac12 x \) could be thought of as another asymptote.