Functions and Graphs

  • Cartesian Coordinate System

    We saw that a point P on a number line can be specified by a real number called its coordinate. Similarly, by using a Cartesian coordinate system, named in honor of the French philosopher and mathematician René Descartes (1596—1650), we can specify a point P in the plane with two real numbers, also called coordinates. […]

  • Algebra Functions

    A function is a rule, correspondence, or mapping that assigns to each real number (the input) in a certain set one and one real number (the output). The set is called the domain of the function, and is the dependent variable, since its value depends on the value of . Because can assign any value […]

  • Graph of a Function

    The graph of a function f is defined to be the graph of the corresponding equation . In other words, the graph is the set of all points in the Cartesian plane such that is in the domain of and . For instance, if m and b are constants, then the graph of the function […]

  • Geometric Properties of Graphs

    The graph in Figure 1 (a) is always rising as we move to the right, a geometric indication that the function is increasing; that is, as increases, so does the value . On the other hand, the graph in Figure 1 (b) is always falling as we move to the right, indicating that the function […]