A function is a relation in which each input has only one output. In the relation , y is a function of x , because for each input x (1, 2, 3, or 0), there is only one output y . x is not a function of y , because the inputy = 3 has multiple outputs: x = 1 andx = 2 .

Examples:
\: y is a function of x , x is a function of y .

: y is not a function of x ( x = 3 has multiple outputs), x is a function of y .

: y is a function of x , x is not a function of y ( y = 9 has multiple outputs).

: y is not a function of x ( x = 1 has multiple outputs), x is not a function of y ( y = 2 has multiple outputs).

To determine whether y is a function of x , given a graph of a relation, use the following criterion: if every vertical lineyou can draw goes through only 1 point, y is a function of x . If you can draw a vertical line that goes through 2 points, yis not a function ofx . This is called the vertical line test.

Example 1: In the following graph, y is a function of x :

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