Final answer:
Adam's function rule (y = -x) could be the function rule for the table.
Step-by-step explanation:
In this question, we are given three possible function rules: y = -x, y = -x², and y = -x² - 2x. We need to determine which one (or ones) could be the function rule for the table.
To do this, we can substitute the given x-values from the table into each of the function rules and compare the resulting y-values to the actual y-values in the table. If the function rule gives the correct y-values for all x-values in the table, then it could be the function rule for the table.
Let's go through each function rule:
Adam's function rule (y = -x):
For x = 1, y = -1. For x = 2, y = -2. For x = 3, y = -3.
Comparing these calculated y-values to the actual y-values in the table, we see that Adam's function rule gives the correct y-values for all x-values in the table. Therefore, Adam's function rule (y = -x) could be the function rule for the table.
Belinda's function rule (y = -x²):
For x = 1, y = -1² = -1. For x = 2, y = -2² = -4. For x = 3, y = -3² = -9.
Comparing these calculated y-values to the actual y-values in the table, we see that Belinda's function rule does not give the correct y-value for x = 3 (-9 instead of -5). Therefore, Belinda's function rule (y = -x²) cannot be the function rule for the table.
Chandra's function rule (y = -x² - 2x):
For x = 1, y = -1² - 2(1) = -1 - 2 = -3. For x = 2, y = -2² - 2(2) = -4 - 4 = -8. For x = 3, y = -3² - 2(3) = -9 - 6 = -15.
Comparing these calculated y-values to the actual y-values in the table, we see that Chandra's function rule does not give the correct y-value for x = 2 (-8 instead of -6). Therefore, Chandra's function rule (y = -x² - 2x) cannot be the function rule for the table.
In summary, the correct answer is Adam's only because only his function rule (y = -x) gives the correct y-values for all x-values in the table.