How to find range?
f(x)=x^2/1-x^2

Question

How to find range?
f(x)=x^2/1-x^2

supernova_sonntag · Answer

I know the answer but I need to understand how to do it.

prathamesh_m · Answer

There's actually no fixed method or algorithm for finding the range. You usually do it using the domain, so first find the domain.

supernova_sonntag · Answer

Domain: $$(-\infty,-1) \cup(-1,1)\cup(1,\infty)$$    

$$x \neq1,-1$$

supernova_sonntag · Answer

what now?

anthonyym · Answer

supernova_sonntag · Answer

The horizontal asymptote is -1?

anthonyym · Answer

Yes, it's y = -1

anthonyym · Answer

So all y-values will be defined for the graph except when y = -1.

agent0smith · Answer

supernova_sonntag · Answer

Oh, so how would I write the answer?
Like $$(-\infty,-1) \cup[0,\infty)$$

agent0smith · Answer

From the graph, that looks exactly right

supernova_sonntag · Answer

okay cool. 
However, my text book answer page says that it is $$(-\infty,\infty)\cup[0,\infty)$$

supernova_sonntag · Answer

is that the same thing?

agent0smith · Answer

That makes absolutely no sense as a range, haha the first part says the range is all real numbers, -infinity to infinity

agent0smith · Answer

I'd bet it was a mistake and the infinity should be -1

supernova_sonntag · Answer

I agree. Thank you!