To solve the problem, let's consider each rule provided and see how it transforms the given inputs to the outputs.
The inputs and outputs given are as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Input} & \text{Output} \\
\hline
3 & 9 \\
\hline
5 & 15 \\
\hline
7 & 21 \\
\hline
\end{array}
\][/tex]
Option A: Add 6 to the input to get the output
For each input:
- Input 3: [tex]\( 3 + 6 = 9 \)[/tex]
- Input 5: [tex]\( 5 + 6 = 11 \)[/tex]
- Input 7: [tex]\( 7 + 6 = 13 \)[/tex]
The outputs from this rule are [tex]\( \{9, 11, 13\} \)[/tex].
Option B: Multiply the input by 3 to get the output
For each input:
- Input 3: [tex]\( 3 \times 3 = 9 \)[/tex]
- Input 5: [tex]\( 5 \times 3 = 15 \)[/tex]
- Input 7: [tex]\( 7 \times 3 = 21 \)[/tex]
The outputs from this rule are [tex]\( \{9, 15, 21\} \)[/tex].
Option C: Multiply the input by 2. Then add 5 to the result to get the output
For each input:
- Input 3: [tex]\( 3 \times 2 + 5 = 6 + 5 = 11 \)[/tex]
- Input 5: [tex]\( 5 \times 2 + 5 = 10 + 5 = 15 \)[/tex]
- Input 7: [tex]\( 7 \times 2 + 5 = 14 + 5 = 19 \)[/tex]
The outputs from this rule are [tex]\( \{11, 15, 19\} \)[/tex].
Now, we need to compare the computed results with the given outputs [tex]\( \{9, 15, 21\} \)[/tex]:
- The outputs from Option A ([tex]\( \{9, 11, 13\} \)[/tex]) do not match the given outputs.
- The outputs from Option B ([tex]\( \{9, 15, 21\} \)[/tex]) match the given outputs perfectly.
- The outputs from Option C ([tex]\( \{11, 15, 19\} \)[/tex]) do not match the given outputs.
Therefore, the correct rule that describes the relationship between the input and output pairs is:
(B) Multiply the input by 3 to get the output.
