Does this set of ordered pairs represent a function? Why or why not?

[tex]\[
\{(-5, -5), (-1, -2), (0, -2), (3, 7), (8, 9)\}
\][/tex]

A. Yes, because there are two \( x \)-values that are the same.
B. No, because one \( x \)-value corresponds to two different \( y \)-values.
C. Yes, because every \( x \)-value corresponds to exactly one \( y \)-value.
D. No, because two of the [tex]\( y \)[/tex]-values are the same.



Answer :

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.