Function


   
 
Test for Functions (Summary)
(a) (i) The relation should be one-one or many-one, and
 
(ii) Every first element is mapped which means that every pre-image should have an image.
 
(b) For graphs:
 
Draw a line parallel to the y-axis. If it cuts the graph only in one point, then the graph represents a function. If it cuts in more than one point then the relation is not a function (because the relation will become one-many and for one value of x we will have two or more values of y).
 
The following graphs represent functions:
 
Function; {(x, y) : y = x + 1}
 
 
Function; f(x) =
 
 
Function; {(x, y):y = x2}
 
 
The following graphs do not represent functions:
 
Not function; {(x, y) ; x2 + y2 = 9}
 
 
Not function;
 
 
Not function; f(x) = {(x, y): x = y2}
 
 
 
     
   
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