Real Valued Function of the Real Variable
Recall that the graph of a function y = f(x) consists of all points (x, f(x)) in the Cartesian plane. Note that in the point (x, f(x)), x is the directed distance from the y-axis, and f(x) is the directed distance from the x-axis .
A function which has either R or one of its subsets as its range is called a real valued function. Further, if its domain is also a subset of R then it is called as a real function.