Answers:
The scatterplot graph is shown below.
The points are
- (-1, -2)
- (1, -1)
- (1, 0)
- (2, 2)
- (3, 2)
No the relation is not a function
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Further Explanation:
The left oval is the input oval known as the domain. It shows the list of all possible inputs (x values).
The right oval is the set of possible y values or outputs. This is the range.
Each point is of the form (x,y). Always list x first. Think alphabetical order.
For example, we have -1 in the input oval point to -2 in the output oval. Therefore, the point (-1, -2) is on the scatterplot.
As another example, 3 is in the domain that leads to 2 in the range. It gives us (3,2) as another point.
The list of all possible points generated this way is shown in the answer section above.
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Now to the question if this is a function or not.
Notice how the input x = 1 leads to the outputs y = -1 and y = 0 at the same time. This is sufficient to say "no it's not a function".
Why not? Because we cannot have any input lead to multiple outputs. Any given input must lead to exactly one and only one output, if we wanted to have a function.
The fact that a single vertical line goes through (1,-1) and (1,0) will show that the points fail the vertical line test; hence it's a visual tool to see we don't have a function.
The graph or scatterplot of the points is shown below.