Are the points (3,2) (8,16) (13,8) (14,14) (20,5) (24,8) (27,2) (31,6) (31,3) a function?

The given relation is not a function.

Step-by-step explanation:

Given the relation: {(3,2) (8,16) (13,8) (14,14) (20,5) (24,8) (27,2) (31,6) (31,3)}

A relation is any set of ordered pairs, which can be thought of as (input, output).

A function is a relation in which no two ordered pairs have the same first component (x-values or input) and different second components (y-values or output).

Another way to find out whether a relation or a set of given points represent a function through the Vertical Line Test.  If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.

To use the vertical-line test, imagine dragging a ruler held vertically across the  graph from left to right. If the graph is that of a function, the edge of the ruler would hit the graph only once for every x -value. If you do this for the given set of points, every vertical line intersects the graph in at most one point, except for the x-value = 31, where the vertical line contains two points (in red dots) in it:  (31,6) and (31,3).  The given graph fails the Vertical Line Test, which means that it is not a function.

Attached is a screenshot of the graph where I performed the Vertical Line Test.  

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europa2433

europa2433

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