To determine if the given set of ordered pairs represents a function, we need to check if each [tex]$x$[/tex]-value corresponds to exactly one [tex]$y$[/tex]-value. A set of ordered pairs represents a function if no [tex]$x$[/tex]-value is repeated with different [tex]$y$[/tex]-values.
The given set of ordered pairs is:
[tex]$
\{(-5,-5), (-1,-2), (0,-2), (3,7), (8,9)\}
$[/tex]
Let's list the [tex]$x$[/tex]-values:
[tex]$
-5, -1, 0, 3, 8
$[/tex]
Now, let's check each [tex]$x$[/tex]-value to see if it pairs with more than one [tex]$y$[/tex]-value:
- [tex]$-5$[/tex] pairs with [tex]$-5$[/tex]
- [tex]$-1$[/tex] pairs with [tex]$-2$[/tex]
- [tex]$0$[/tex] pairs with [tex]$-2$[/tex]
- [tex]$3$[/tex] pairs with [tex]$7$[/tex]
- [tex]$8$[/tex] pairs with [tex]$9$[/tex]
We see that each [tex]$x$[/tex]-value is paired with exactly one [tex]$y$[/tex]-value. There are no [tex]$x$[/tex]-values that are repeated with different [tex]$y$[/tex]-values.
Thus, the given set of ordered pairs does represent a function because every [tex]$x$[/tex]-value corresponds to exactly one [tex]$y$[/tex]-value.
Therefore, the answer is:
C. Yes, because every [tex]$x$[/tex]-value corresponds to exactly one [tex]$y$[/tex]-value.
