Recall the meaning of the provided words in order to be able to use them on a description telling why the given graph does not correspond to a function.
Function: A function is a relation where each element in the domain is related to just one element in the range.
Relation: A relation is a correspondence between elements from a set A (the domain of the relation) to elements on a set B (the range of the relation).
Vertical line test: It is a test that can be performed on the graph of a relation to check if it is a function or not. If there is no vertical line such that it crosses the graph of the function two or more times, then the relation is a function (each vertical line should cross the graph of a function at most one time).
X-value: Is a value over the horizontal axis.
Y-value: Is a value over the vertical axis.
Correspondence: a link between two or more objects.
Open circle: Is used on graphs to represent points that are not included in the function.
Closed circle: is used on graphs to represents points that are included in the function.
Domain: The domain of a function or relation is the set of all possible inputs for the function or relation.
Range: The range of a function or relation is the set of all possible values that the function or relation can take when evaluated at an element from the domain.
Taking all these considerations into account, notice the following:
The vertical line test shows that for the value of 6 in the domain of the relation, a vertical line cuts the graph twice, since there are two closed circles at the values of 3 and 4 in the range of the relation. Therefore, the given graph does not correspond to the graph of a function.