For each graph below, state whether it represents a function.
WHY ARE THERE DOTS. SOMEONE PLEASE EXPLAIN!

  1, 2, 4 -- not a function

  3, 5, 6 -- a function

Step-by-step explanation:

A relation can be represented many ways. Among these are ...

A list of ordered pairs is a set of point ("dots") when it is plotted on a coordinate plane. That is, a graph with dots represents a relation.

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A relation is a function when there is exactly one output value for each input value. Output values are plotted vertically, and input values are plotted horizontally. So, a relation that is a function cannot have a graph that has one point above (or below) another.

Graphs 1 and 2 have lines above/below each other. They are not graphs of functions. Graph 4 has a pair of dot above/below each other (at (-2, -1) and (-2, -4)), so it is not a function, either. You cannot draw a vertical line through these graphs (everywhere) without running into two output values for the same input value.

The remaining graphs pass this "vertical line test" so do represent relations that are functions.

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Graph 3 has a closed dot above an open dot. The value of the function for that x-value is the value of the closed dot. The open dot means the function is not defined at that particular point. Since the relation only has one output value there, it is a function.

Short story: a graph that intersects any vertical line in only one place is the graph of a function. A list of ordered pairs, or a table, in which any input value appears 2 or more times is not a function. Likewise, a graph with multiple output values for one input value is not a function.

step-by-step explanation: