I am absolutely horrible with graphs and things involving infinity. I'm just confused about most of it tbh. If any of y'all can help that would be great thx :)

I was helping my nephew with functions but i was stumped with why parts of the quadratic equations were used for 6.5 and 6.5. Help, please.

Apparently the answer is (d) but I have no idea how to get there

What method should I use and how should I go about solving this?