Question

Question 17 (4 points)

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The set of ordered pairs shown is missing an x-value.
(9,-15),(0,0),(4,0),(_,2)


Give an x-value that make the relation not a function. You must show ALL work to earn full credit.

Answer 1

To determine an x-value that would make the relation not a function, we need to first understand what constitutes a function. A relation is considered a function if each input (x-value) has exactly one output (y-value). In other words, for any given x-value, there should not be more than one corresponding y-value.

Let’s analyze the given ordered pairs:

1. (9, -15)
2. (0, 0)
3. (4, 0)
4. (_, 2) – here, '_' is the missing x-value.

Now, looking at the ordered pairs already provided, we have three distinct x-values: 9, 0, and 4. To make the relation not a function, we need to pick a new x-value that already appears with a different y-value.

The x-value options that we have are:
- 9 (with y = -15)
- 0 (with y = 0)
- 4 (with y = 0)

To cause this relation to not be a function, we could assign the missing x-value ('_') to be one of the existing x-values and pair it with a different y-value than the one currently assigned to it.

Let’s choose **0** as the x-value for the missing pair, so the ordered pair would be (0, 2).

Now we have the pairs:

1. (9, -15)
2. (0, 0)
3. (4, 0)
4. (0, 2)

Here, x = 0 is associated with two different y-values (0 and 2). This violates the definition of a function because a single input (x = 0) corresponds to two outputs (y = 0, and y = 2).

Therefore, the x-value that makes the relation not a function is:

**0**

So the resulting ordered pairs would be (9, -15), (0, 0), (4, 0), (0, 2).