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Question

How do you tell if the relation is a function ?


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Solution

To determine if relation is a function:

A relation is said to be a function if for each value of the independent variable x; there is only one possible value of y, i.e. the dependent variable. In other words we can say, for each input value of x, there should be only one output value.

We can also check graphically whether the relation is a function or not using a vertical line test. Draw a vertical line anywhere, if the vertical line cross the graph at exactly one point then it is a function.

When we observe a set of pairs of numbers (set of ordered pairs) in the form (x,y) and if any of the yvalues are repeated, then it is not a function. Thus we can say that all functions are relations, but not all the relations are functions.

Hence, we can tell if the relation is a function by above three ways.


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