Cumulative Assessment
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When a set of data represents a function, there is exactly one output value for each corresponding input.
Example Solution:
Our claim
| x | -4 | -3 | -2 | -1 | 0 |
|---|---|---|---|---|---|
| y | 0 | 1 | 2 | 3 | 4 |
Friend's claim
| x | -3 | -3 | -2 | -1 | 0 |
|---|---|---|---|---|---|
| y | 0 | 1 | 2 | 3 | 4 |
Let's choose the values to support our claim first, and then we will rearrange them to support our friend's claim. Keep in mind that this is just one possible answer for this problem.
Let's recall an important rule about functions.
|
A function is a relation in which each input value corresponds to exactly one output value. |
| x | -4 | -3 | -2 | -1 | 0 |
|---|---|---|---|---|---|
| y | 0 | 1 | 2 | 3 | 4 |
For each x-value, we have exactly one y-value. Therefore, this is a function.
For a relation not to be a function, at least one input value has to correspond with two or more output values. To create this, we can delete one of the inputs from our table and substitute it with another existing x-value. Let's substitute x=-4 with x=-3.
| x | -3 | -3 | -2 | -1 | 0 |
|---|---|---|---|---|---|
| y | 0 | 1 | 2 | 3 | 4 |
Let's graph this relation and use the Vertical Line Test.
Since there are two corresponding y-values for x=-3, this relation is not a function.