## The graph of a function.

Let be a real function of a real variable , defined over a domain in . The set of points in the plane whose coordinates are , for is called the graph of .

Example 2.5.1   In figure we display the graphs of the absolute value function ( ) and of the floor function (=integer part function: ). In figure we display the graphs of two other well-known functions; these graphs are a parabola and an hyperbola, respectively. The curves in figure 4 are not graphs of functions. Dear reader, why? We will make great use of graphs. On the one hand, they provide a good visual intuition of the phenomena described by the fuctions. On the other hand, applied scientists are often able to draw a graph representing the phenomenon that they study, even when the actual function is still unknown. From the study of the graph they can get many useful conclusions.

Noah Dana-Picard 2007-12-28
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