Sure, let's match each function to its correct range given the domain [tex]$\{1, 2\}$[/tex]:
1. Function: [tex]\( f(x) = 3x + 5 \)[/tex]
- Range: \{8, 11\}
2. Function: [tex]\( f(x) = x^2 - 2x - 5 \)[/tex]
- Range: \{-6, -5\}
3. Function: [tex]\( f(x) = (x + 5)x^2 \)[/tex]
- Range: \{6, 28\}
4. Function: [tex]\( f(x) = 4 - x \)[/tex]
- Range: \{2, 3\}
Therefore, we can pair the functions and their ranges as follows:
- [tex]\( f(x) = 3x + 5 \)[/tex] corresponds to \{8, 11\}
- [tex]\( f(x) = x^2 - 2x - 5 \)[/tex] corresponds to \{-6, -5\}
- [tex]\( f(x) = (x + 5)x^2 \)[/tex] corresponds to \{6, 28\}
- [tex]\( f(x) = 4 - x \)[/tex] corresponds to \{2, 3\}
So the correct matches are:
- [tex]\( \{8, 11\} \)[/tex] ⟹ [tex]\( f(x) = 3x + 5 \)[/tex]
- [tex]\( \{ -6, -5 \} \)[/tex] ⟹ [tex]\( f(x) = x^2 - 2x - 5 \)[/tex]
- [tex]\( \{6, 28\} \)[/tex] ⟹ [tex]\( f(x) = (x + 5)x^2 \)[/tex]
- [tex]\( \{2, 3\} \)[/tex] ⟹ [tex]\( f(x) = 4 - x \)[/tex]
