Question

On a coordinate plane, solid circles appear at the following points: (negative 2, negative 5), (negative 1, 3), (1, negative 2), (3, 0), (4, negative 2), (4, 4). Which explains why the graph is not a function? It is not a function because the points are not connected to each other. It is not a function because the points are not related by a single equation. It is not a function because there are two different x-values for a single y-value. It is not a function because there are two different y-values for a single x-value.

Answer 1

Last option: It is not a function because there are two different y-values for a single x-value.

Explanation:

It is necessary to remember that, by definition, a relation is a function if each input value (x-value) has one and only one output value (x-value) .

In this case, the following points:

`(-2, -5), (- 1, 3), (1, -2), (3, 0), (4,- 2), (4, 4)`

You can observe that the input value 4 (
`x=4`) has two ouput values. These are:

`y=-2\\\\ y=4`

Therefore, since there are two different y-values for a single x-value, you can conclude that the given graph is not a function.