To determine which ordered pair, if any, needs to be removed so that the mapping represents a function, we need to consider the definition of a function. A function is defined such that each input (or domain element) maps to exactly one output (or range element). In other words, there should be no repeated x-values with different y-values.
We have the following ordered pairs:
[tex]$
(-3, -4), (-2, -1), (1, -3), (3, 7)
$[/tex]
Let's analyze these pairs step-by-step to check if any x-values are repeated:
1. The first pair is [tex]\((-3, -4)\)[/tex].
2. The second pair is [tex]\((-2, -1)\)[/tex].
3. The third pair is [tex]\((1, -3)\)[/tex].
4. The fourth pair is [tex]\((3, 7)\)[/tex].
Now, we will check the x-values:
- [tex]\(-3\)[/tex] (from the pair [tex]\((-3, -4)\)[/tex])
- [tex]\(-2\)[/tex] (from the pair [tex]\((-2, -1)\)[/tex])
- [tex]\(1\)[/tex] (from the pair [tex]\((1, -3)\)[/tex])
- [tex]\(3\)[/tex] (from the pair [tex]\((3, 7)\)[/tex])
Each x-value is unique in this list. Since all x-values are different, there are no repeated x-values with different y-values. This means that each input maps to a unique output without any duplications or conflicts.
Therefore, based on this analysis, all the pairs satisfy the condition of being a function.
As a result, no ordered pair needs to be removed.
So, the correct answer is:
[tex]$
0.
$[/tex]
