Test for Functions

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Following are the test for Functions

(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}