. Representation of Functions A function may be represented by (a) a set of ordered pairs (b) a table form (c) an arrow diagram (d) a graphical form Let f : ® be a function (a) Set of ordered pairs The set f f x ∈ { | ( ), } of all ordered pairs represent a function. (b) Table form The values of x and the values of their respective images under f can be given in the form of a table . (c) Arrow diagram An arrow diagram indicates the elements of the domain of f and their respective images by means of arrows.
(d) Graph The ordered pairs in the collection f f x ∈ {( ) | } ( ), are plotted as points in the XY - plane. The graph of f is the totality of all such points. Every function can be represented by a curve in a graph. But not every curve drawn in a graph will represent a function.
The following test will help us in determining whether a given curve is a function or not. . . Vertical line test A curve drawn in a graph represents a function, if every vertical line intersects the curve at only one point.
Example . Using vertical line test, determine which of the following curves (Fig. . (a), .
(b), . (c), . (d)) represent a function? X ¢ Fig.
. (c) - - - - X ′ P Q - - - - - - - Solution The curves in Fig. . ( a ) and Fig.
. ( c ) do not represent a function as the vertical lines meet the curves in two points P and Q . The curves in Fig. .
(b) and Fig. . (d) represent a function as the vertical lines meet the curve in at most one point.