Thread: How can i find the limits of this function/equation?

Hello!
I have no idea where to post this so I'll just put it here.

The function f(x)= 1 - [2x/(1+(x^2))]
Sorry if this is confusing, ive written it all out on paint so please open the attached file

QUESTION:
to display the graph of y=f(x) for -10<x<10, a suitable interval for y, a<x<b must be chosen. Suggest appropriate values for a and b.

I would suppose that you substitute x=-10 and x=10 to find a and b accordingly yet I cant get the right answer


Thank you!

For one, you just look at it. Imagine what it does at its extremes.

If x increases without bound, getting larger and larger...

a) What does '1' do? Nothing.
b) What does the rational expression do? It shrinks. This piece disappears.
c) So, we seem to be sneaking up on x = 1 from the bottom.

If x decreases without bound, getting larger and larger in the negative direction...

a) What does '1' do? Nothing.
b) What does the rational expression do? It shrinks. This piece disappears.
c) So, we seem to be sneaking up on x = 1 from the top.

We just defined an horizontal asymptote. x = 1.

What do you suppose is next?