The graph of a function f is defined to be the graph of the corresponding equation y=f(x). In other words, the graph f is the set of all points (x, y) in the Cartesian plane such that x is in the domain of f and y=f(x).

            For instance, if m and b are constants, then the graph of the function f(x) = mx + b is the same as the graph of the equation y = mx + b, a line with slope m and y intercept b (as shown in the figure). For this reason, a function of the form f(x) = mx + b is called a linear function.
            Graph of functions that are not linear are often (but not always) smooth curves in the Cartesian plane.

The Vertical-Line Test:
            A set of points in the Cartesian plane is the graph of a function if and only if no vertical straight line intersects the set more than once.