To determine if the given relation is a function, we need to check if each input (or "x-value") from the set of pairs corresponds to exactly one output (or "y-value"). A relation is considered a function if no x-value is repeated with different y-values.
The given relation is:
[tex]\[
\{(3,-5),(1,2),(-1,-4),(-2,2)\}
\][/tex]
Let's list the x-values in this relation:
- For the pair [tex]\((3, -5)\)[/tex], the x-value is [tex]\(3\)[/tex].
- For the pair [tex]\((1, 2)\)[/tex], the x-value is [tex]\(1\)[/tex].
- For the pair [tex]\((-1, -4)\)[/tex], the x-value is [tex]\(-1\)[/tex].
- For the pair [tex]\((-2, 2)\)[/tex], the x-value is [tex]\(-2\)[/tex].
Next, we check if any of these x-values are repeated:
- The x-value [tex]\(3\)[/tex] appears once.
- The x-value [tex]\(1\)[/tex] appears once.
- The x-value [tex]\(-1\)[/tex] appears once.
- The x-value [tex]\(-2\)[/tex] appears once.
Since none of the x-values are repeated, each x-value is associated with exactly one y-value. Therefore, the relation satisfies the criteria for being a function.
Based on this analysis, the answer is:
Yes
