Thedomainof a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function. It is the set of all real numbers for which a function is mathematically defined.
The rangeof a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
To find the domain
In general, we determine the domain of each function by looking for those values of the independent variable (usually x) which we are allowed to use. (Usually we have to avoid 0 on the bottom of a fraction, or negative values under the square root sign).
To find the range
The range of a function is the spread of possible y-values (minimum y-value to maximum y-value)
Substitute different x-values into the expression for y to get the range of function.