Domain and range of a multiple non-connected lines from a function? How do you find the domain and range of a function that has multiple non-connected lines? 
Such as, $ f(x)=\sqrt{x^2-1}$. Its graph looks like this:


I'm wanting how you would write this with a set eg: $(-\infty, \infty)$.
P.S. help me out with the title. Not sure how to describe this.

You can find domain of the function by simply analyzing the behavior of the function. For 
$$
f(x) = \sqrt{x^2-1}
$$
you can conclude that the expression under the square root must be non-negative. So
$$
x^2-1 \ge 0 \\
(x-1)(x+1) \ge 0 \\
x \in (-\infty, -1] \cup [1, +\infty)
$$
Latter is your domain. $D[f] = (-\infty, -1] \cup [1, +\infty)$
Finding range of the function sometimes is more trickier, but for this particular function not so much. Again, you have to observe its behavior. It's square root, and square root in real analysis can take any non-negative value, so range is $E[f] = [0, +\infty)$.
