Some of the domain problems can be solved by examining denominators, etc.  These types of problems are really more a test of understanding the definitions of "domain" and "range". The domain of a function are the legal values one can put into the function and one typically is looking for radicals [can't take a negative square root] or fractions [can't divide by zero] to determine the domain of a function. The range of a function is the set of all values a function is able to produce.

The mathematical approach taken by the software when solving for the range of a function is to find the inverse of a function and then calculate its domain - if no inverse is present, then simply determine the answer graphically. Parabolic functions do not have an inverse function, so the range should simply be determined graphically. If you will notice in the graph that the largest value for "y" is 7, therefore the range of the function is (-inf, 7] because y can become infinitely small.

For such topic-focused contents, you might wish to review Algebrator, through which many additional tools are available (an example solution is show imaged below):

Windows: http://www.softmath.com/tr/alg51win-tr-en.exe

Mac: http://www.softmath.com/tr/alg51mac-tr-en.dmg