To determine which function satisfies [tex]\( y = 2 \)[/tex] when [tex]\( x = 3 \)[/tex], we'll evaluate each given function at [tex]\( x = 3 \)[/tex] and see if the result equals [tex]\( 2 \)[/tex].
### Function 1: [tex]\( -\frac{(x-5)}{(x+3)} \)[/tex]
Evaluate at [tex]\( x = 3 \)[/tex]:
[tex]\[
-\frac{(3-5)}{(3+3)} = -\frac{(-2)}{6} = \frac{2}{6} = \frac{1}{3}
\][/tex]
This does not equal [tex]\( 2 \)[/tex].
### Function 2: [tex]\( \pi(x) = \frac{2(x+5)}{(x+3)} \)[/tex]
Evaluate at [tex]\( x = 3 \)[/tex]:
[tex]\[
\frac{2(3+5)}{(3+3)} = \frac{2(8)}{6} = \frac{16}{6} = \frac{8}{3}
\][/tex]
This does not equal [tex]\( 2 \)[/tex].
### Function 3: [tex]\( f(x) = \frac{2(x+5)}{(x-3)} \)[/tex]
Evaluate at [tex]\( x = 3 \)[/tex]:
[tex]\[
\frac{2(3+5)}{(3-3)} = \frac{2(8)}{0}
\][/tex]
This is undefined, as division by zero is not possible.
### Function 4: [tex]\( -\frac{(x+5)}{(x-3)} \)[/tex]
Evaluate at [tex]\( x = 3 \)[/tex]:
[tex]\[
-\frac{(3+5)}{(3-3)} = -\frac{8}{0}
\][/tex]
This is undefined, as division by zero is not possible.
Since none of the functions return [tex]\( y = 2 \)[/tex] when [tex]\( x = 3 \)[/tex], there seems to be no function from the set provided that satisfies both [tex]\( x = 3 \)[/tex] and [tex]\( y = 2 \)[/tex].
### Conclusion:
None of the functions provided has both an appropriate domain where [tex]\( x = 3 \)[/tex] and a range that includes [tex]\( y = 2 \)[/tex].
