Functions, Domain and Codomain
A functiontakes a numberand returns the valuecorresponding to that number. We can plot the pointas ordinary points. In fact we can plot one pointfor each allowed value ofand hence obtain the graph ofThe graph of the functionis shown below.
Some definitions are necessary:
The domain of a function is the set of values thatcan take. We can read the domain off the– axis. For the functionthe domain is the set of all real numbers but forwe may not havebecause that would result in the divisionwhich is not defined. If for any reason the possible set of values ofis restricted to certain values, for examplethen that is the domain.
Range or Codomain
The range or codomain of a function is the set of values the functionmay take. We read the codomain off the– axis. For the functionthe codomain is the set of all real numbers becausemay take any value, or alternatively, the equationhas a solution for allvalues. Forwe may not havebecausehas no solutions forIf for any reason the possible set of values ofis restricted to certain values, for examplethen that may restrict the codomain: forifthen
Withto evaluatewhenwe find