A table representing a relation is shown.

x y
-1 3
-2 1
a 4
-3 2
What value of a would result in the table NOT representing a function?
a =

1 answer

For a relation to be considered a function, each input (x-value) must correspond to exactly one output (y-value). This means that no two different inputs can have the same output.

In the table you provided, we have the following x-values:

  • -1
  • -2
  • a
  • -3

If we want the relation to not represent a function, we need the value of \( a \) to be such that it matches one of the existing x-values, which would create a situation where one input (the repeated x-value) corresponds to multiple outputs (potentially).

The existing x-values are -1, -2, and -3. Therefore, if \( a \) takes on one of these values, the relation will not be a function.

Thus, the possible values of \( a \) that would result in the table NOT representing a function are:

  • \( a = -1 \)
  • \( a = -2 \)
  • \( a = -3 \)

Any of these values will satisfy the condition. Therefore, the answer is:

\( a = -1 \), \( a = -2 \), or \( a = -3 \).

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