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Adam says that the function rule is y=-x, Belinda says that the function rule is y=-x², and Chandra says that the function rule is y=-x²-2x. Which of the three equations could be the function rule for the table?

1) Adam's only
2) Adam's and Chandra's only
3) Belinda's and Chandra's only
4) Adam's, Belinda's, and Chandra's

User Zepplock
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1 Answer

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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.

User Ender Che
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