Let's determine the relationship between the inputs and outputs by analyzing each suggested relationship step-by-step.
### Relationship 1: "Divide by 2, then add 5"
1. For input 12:
[tex]\[
\left(\frac{12}{2}\right) + 5 = 6 + 5 = 11 \quad \text{(Matches output 11)}
\][/tex]
2. For input 14:
[tex]\[
\left(\frac{14}{2}\right) + 5 = 7 + 5 = 12 \quad \text{(Matches output 12)}
\][/tex]
3. For input 16:
[tex]\[
\left(\frac{16}{2}\right) + 5 = 8 + 5 = 13 \quad \text{(Matches output 13)}
\][/tex]
4. For input 18:
[tex]\[
\left(\frac{18}{2}\right) + 5 = 9 + 5 = 14 \quad \text{(Matches output 14)}
\][/tex]
Since all input-output pairs match using this relationship, this appears to be a potential correct relationship.
### Relationship 2: "Subtract 1"
1. For input 12:
[tex]\[
12 - 1 = 11 \quad \text{(Matches output 11)}
\][/tex]
2. For input 14:
[tex]\[
14 - 1 = 13 \quad \text{(Does not match output 12)}
\][/tex]
Since this relationship does not hold for input 14, it is not the correct relationship.
### Relationship 3: "Subtract 2"
1. For input 12:
[tex]\[
12 - 2 = 10 \quad \text{(Does not match output 11)}
\][/tex]
Since the first pair does not match, this relationship is incorrect.
### Relationship 4: "Add 5, then divide by 3"
1. For input 12:
[tex]\[
\left(\frac{12 + 5}{3}\right) = \left(\frac{17}{3}\right) = 5.\overline{66} \quad \text{(Does not match output 11)}
\][/tex]
Since the first pair does not match, this relationship is incorrect.
Based on this step-by-step examination, the correct relationship between the inputs and outputs in the given table is:
"Divide by 2, then add 5."
This is confirmed as the correct relationship fits all input-output pairs.
