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.