What is the domain and range of #y = -sqrt(x ^2 - 3x - 10)#?
Domain: the union of two intervals:
Domain is a set of argument values where the function is defined. In this case we deal with a square root as the only restrictive component of the function. So, the expression under the square root must be non-negative for the function to be defined.
Therefore, the domain of the original function is the union of two intervals:
Inside each of these intervals the expression under a square root changes from
Hence, the range of this function is