Functions, Domain and Codomain

A function takes a number and returns the value corresponding to that number. We can plot the point as ordinary points. In fact we can plot one point for each allowed value of and hence obtain the graph of The graph of the function is shown below. Some definitions are necessary:

Domain

The domain of a function is the set of values that can take. We can read the domain off the – axis. For the function the domain is the set of all real numbers but for we may not have because that would result in the division which is not defined. If for any reason the possible set of values of is restricted to certain values, for example then that is the domain.

Range or Codomain

The range or codomain of a function is the set of values the function may take. We read the codomain off the – axis. For the function the codomain is the set of all real numbers because may take any value, or alternatively, the equation has a solution for all values. For we may not have because has no solutions for If for any reason the possible set of values of is restricted to certain values, for example then that may restrict the codomain: for if then With to evaluate when we find  