Question

Which of the following values could be used for x and would cause the following relation to NOT be a function?

{(2,3), (-2,6), (-4,-4), (x, 2), (5,-9)}

(1 point)
Responses

x = 0
x = 0

x=3
x=3

x = 6
x = 6

x = -4

Answer 1

To determine which value of \( x \) would cause the relation to NOT be a function, we need to remember that a relation is a function if each input (first component of each ordered pair) corresponds to exactly one output (second component of each ordered pair).

In this case, we are given the relation:

\[
\{(2,3), (-2,6), (-4,-4), (x, 2), (5,-9)\}
\]

The key here is to check if any of the values for \( x \) given in the options would create a situation where an input would map to multiple outputs.

Now, let's analyze the options:

1. **\( x = 0 \)**: The relation becomes \((2,3), (-2,6), (-4,-4), (0, 2), (5,-9)\). No conflicts, so this remains a function.

2. **\( x = 3 \)**: The relation becomes \((2,3), (-2,6), (-4,-4), (3, 2), (5,-9)\). No conflicts, so this remains a function.

3. **\( x = 6 \)**: The relation becomes \((2,3), (-2,6), (-4,-4), (6, 2), (5,-9)\). No conflicts, so this remains a function.

4. **\( x = -4 \)**: The relation becomes \((2,3), (-2,6), (-4,-4), (-4, 2), (5,-9)\). Here, the input \(-4\) corresponds to two different outputs: \(-4\) and \(2\). This violates the definition of a function.

Thus, the value of \( x \) that would cause the relation to NOT be a function is:

**\( x = -4 \)**.