•Given a relation in x and y, we say y is a function of x if for each element x in the domain, there is exactly one value of y in the range. It is a rule of correspondence between two nonempty sets, such that, to each element of the first is called domain, there correspondents one and only one element of the second is called range. Read the details about function notation inTo determine whether it is function or not by using the vertical line test. If the graph passed to Vertical line test it is consider as function. The graph of function defines y as a function of x if no vertical line intersects the graph in more than one point. Here are the example of function and not function
1. The first set of ordered pairs is a function, because no two ordered pairs have the same first coordinates with different second coordinates for example ( -1, 2), ( 1, 0), (2, 1) .
2. The second example is not a function, because it contains the ordered pairs (1,2) (1,4)( 2, -1). the first set is repeated . These have the same first coordinate and different second coordinates. Read the details about the set of ordered pairs inThe range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. The range is the resulting y-values we get after substituting all the possible x-values. Read the details about the definition of range in