Functions, domain and range

A function is a relation between a set of inputs and a set of permissible outputs such that each input is related to exactly one output. The domain is the set of permitted inputs. The codomain is the permissible target set, while the range is the set of outputs actually attained; hence the range is a subset of the codomain. In this mapping, the outputs attained are y_1,y_2,y_3,y_4; y_5 lies in the codomain but not the range. Function notation names the input: C(n)=4n+7 can model the cost of n items. If at most 20 items can be ordered, the practical domain is n in 0,1,,20, not every real number. Without a stated restriction, use the largest real domain where the formula is defined. Denominators cannot be zero, logarithm arguments must be positive and real square-root arguments must be non-negative. Example For f(x)=sqrt(x-3), the domain is [3,infinity) and range is [0,infinity).