4x

X
Y
-5
-1
-6
9
5
2
3
6
9
6
The table shows y as a function of x. Suppose a point is added to this table. Which choice gives a point that preserves the function?

A
(9, 8)

B
(-6, 3)

C
(-5, -2)

D
(-3, - 8)

1 answer

To determine which choice provides a point that preserves the function (i.e., adheres to the rule of a function where each x-value must correspond to exactly one y-value), we need to check if the x-value of each choice already exists in the original set of x-values.

From the given data, the unique x-values already present are:

  • 4
  • -5
  • -1
  • -6
  • 9
  • 5
  • 2
  • 3
  • 6

Now we analyze each option:

A. (9, 8) - The x-value 9 already exists in the table, so this would conflict with the rule of a function. B. (-6, 3) - The x-value -6 already exists, so this would conflict as well. C. (-5, -2) - The x-value -5 already exists, leading to a conflict. D. (-3, -8) - The x-value -3 does not appear in the current set of x-values, meaning this is not in conflict with the existing data.

Thus, the only choice that gives a point that preserves the function is:

D. (-3, -8).