Graphing function and its reciprocal, also get domain/range

Hello.

I have the function y=x^2 - 3

Would the reciprocal be: y= 1/(x^2-3)?

(I need to graph these by hand without a graphing calculator.)

Now how would I graph y=x^2-3?

The -3 tells me the min of the range is -3? So I start at -3 and go up, but how do I know how wide to make it or where to make the zeroes?

Same thing for the reciprocal, I have no idea to graph that and find the range/domains of it too.

Any help would be greatly appreciated.