Thread: Domain, range, and equation for horizontal and vertical asymptotes?

Can someone explain how to find those for:
y = 1 / (x^2 + 2) - 1


Correct me if I'm wrong, but the domain is all numbers X cannot be, the range is all numbers Y can be but I am unsure on how to find them and unsure of what asymptotes are and how to find those too.

Originally Posted by olen12

Can someone explain how to find those for:
y = 1 / (x^2 + 2) - 1


Correct me if I'm wrong, but the domain is all numbers X cannot be, the range is all numbers Y can be but I am unsure on how to find them and unsure of what asymptotes are and how to find those too.

Let's asume that

f is defined on R, because there isn't any x so





So x raises from -infinity to 0 and deacreases from 0 to +infinity
Which means that 0 is an local maxima




So f has y=-1 horizontal asymptote.

There isn't any real number a, so

Which means f doesn't have vertical asymptote.
f doesen't have oblical asymptote neither.

Hi, thanks for the help but a few things I don't understand.

What does 'lim' mean?

And what is R?

Originally Posted by olen12

Hi, thanks for the help but a few things I don't understand.

What does 'lim' mean?

And what is R?

lim means the limit, or more specifically, the limit of a function as x approaches a particular value. R denotes the set of all real numbers. Saying that "the domain of the function is R" means "the function is defined for all real values of x."