Question

For the following relation to be a function, x cannot be what values?
{(3, 6), (4, 8), (x, 10), (6, 12) }
3
5
7

Answer 1

For a relation to be considered a function, each input (in this case, each \( x \) value) must correspond to exactly one output. In the given set of ordered pairs { (3, 6), (4, 8), (x, 10), (6, 12) }, we need to determine what values \( x \) can take so that it does not repeat any of the existing \( x \) values in the set.

The current \( x \) values in the relation are 3, 4, and 6. If we assign \( x \) a value that is already in the set (that is, 3, 4, or 6), it will violate the rule of a function, because there will then be two different outputs for the same input.

Thus, for the relation to remain a function, \( x \) cannot be:
- 3
- 4
- 6

Among the choices provided (3, 5, 7), the values that \( x \) absolutely cannot be for the relation to remain a function are:
- 3 (since it already exists)
- 4 (since it already exists)
- 6 (since it already exists)

5 and 7 are acceptable since they do not conflict with any existing \( x \) value.

Therefore, \( x \) cannot be **3, 4, or 6**, and from the given options specifically, it **cannot be 3.**