Is the following relation graphed below a function? Explain? Think about what open and closed circles mean

Given:

The graph of a relation.

To find:

Whether the given relation in the graph is a function or not.

Solution:

First we need to understand the meaning of open circles and closed circles.

Open circle: It is a unfilled circle, it means, that value is not included in the solution set.

Close circle: It is a completely filled circle, it means, that value is included in the solution set.

A relation is a function if their exist a unique y-value (output value) for each x-value (input value).

The graph of a relation is a function, if the graph intersect each vertical line at most once. It is known as vertical line test.

For the vertical lines x=-1 and x=1, the graph has only one close circle and all other vertical line intersect the graph at most once.

Since the graph passes the vertical line test, therefore it represents a function.

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