The Student Room Group

C3- How to find the range of a reciprocal function?

Hello, this has always been a topic that has confused me. Can someone please explain how I can find the range of a function which is a reciprocal function? For example, what would be the range of (2x+1)/(x-3) and how would this be worked out? A step by step explanation would be very helpful indeed. I understand how to find the domain but its always the range that has confused me.

Also, can someone please explain how to find asymptotes on these types of graphs?

Any help much appreciated.

Thanks :smile:

EDIT: Also, can anyone please explain how I would go about drawing these sorts of graphs as well? Thanks.
Reply 1
x=3 will cause trouble - right?

The function is undefined there, but seems to be defined on all other places - agreed?

To draw the function, look for stationary points(f'=0, mostly), asymptotes (vertical when zero denominator, to find oblique look at limx[f(x)x]lim_{x\to\infty}[f(x)-x] and limx[f(x)x]lim_{x\to\infty}[\frac{f(x)}{x}]) and where the function is concave/convex (f'')