Cumulative Assessment
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When a set of data represents a linear function, the rate of change is constant. Create a table that supports your claim, then rearrange it to have a table that supports your friend's claim.
Example solution:
Your Claim
| x | y |
|---|---|
| -4 | 1 |
| -3 | 2 |
| -2 | 3 |
| -1 | 4 |
Friend's Claim
| x | y |
|---|---|
| -4 | 2 |
| -3 | 1 |
| -2 | 3 |
| -1 | 4 |
Let's choose the values to support our claim first, then rearrange them to support our friend's claim. Keep in mind that our tables will be just one possible answer for this problem.
We want to create a table of values that represents a linear function, which means the rate of change has to be constant. From the given numbers, we see that both the top and the bottom tiles increase by 1.
Top Row:& - 4 +1 → - 3 +1 → - 2 +1 → - 1 +1 → 0
Bottom Row:& 1 +1 → 2 +1 → 3 +1 → 4 +1 → 5
| x | y |
|---|---|
| -4 | 1 |
| -3 | 2 |
| -2 | 3 |
| -1 | 4 |
When x increases by 1 the value of y increases by 1. Therefore, this is a linear function.
Our friend wants to create a table of values that represents a nonlinear function. This means that the rate of change will not be constant. To do this, we can exchange 2 of the y-values from the table that supported our claim. Let's switch y=1 with y=2.
| x | y |
|---|---|
| -4 | 2 |
| -3 | 1 |
| -2 | 3 |
| -1 | 4 |
Now the rate of change is not constant, so it is a nonlinear function.