Functions, Domain and Codomain
A function
takes a number
and returns the valuecorresponding to that number. We can plot the point
as ordinary points. In fact we can plot one pointfor each allowed value ofand 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 thatcan take. We can read the domain off the– axis. For the functionthe 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 ofis 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 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 equation
has a solution for allvalues. Forwe may not have
because
has no solutions for
If for any reason the possible set of values ofis restricted to certain values, for example
then that may restrict the codomain: for
ifthen
With
to evaluatewhen
we find
