Question

How do you find the domain and range of `y = sqrt( x^2 +4) /( x^2 - 4)`?

Answer 1

Domain: (-infinity, -2] U [2, infinity). In other words, domain is all real numbers except for when x= 2, and -2.
Range: (-infinity, infinity). Which is all real numbers.

Explanation:

Solve for x on the denominator by setting x^2 -4 =0. You should get x=2, -2. Which means that there are vertical asymptotes at 2 and -2.