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Which relation is a function?

Which relation is a function?-example-1

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Answer:

1st option (parabola) represents a function

Explanation:

A relation is a function if each element of X is related to exactly one element in Y. That is, given an element x in X, there is only one element in Y that x is related to.

To check whether a relation is a function, you can apply vertical line test. For an arbitrary x, draw vertical line and this line must intersect the graph of the relation at exactly one point.

Check all options:

1. Each vertical line intersects the graph of the relation at exactly one point - this is a function.

2. The graph shows vertical line x = 3. So, there are infinitely many points of intersection - this is not a function.

3. For all x > 0, vertical lines intersect the graph of the relation in two distinct points - this is not a function.

4. Vertical lines intersect circle at two points (except points where circle intersects x-axis) - this is not a function.

User Lazar Nikolov
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