To determine the rule that best describes the relationship between the given input and output pairs in the table, we will systematically verify each provided rule against all input-output pairs.
The table given is:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Input} & \text{Output} \\
\hline
9 & 7 \\
8 & 5 \\
7 & 3 \\
\hline
\end{array}
\][/tex]
We need to check each provided rule:
### Rule (A): Subtract 2 from the input to get the output.
Let's apply this rule to each input:
- For input 9: [tex]\( 9 - 2 = 7 \)[/tex] → Output is 7 (matches)
- For input 8: [tex]\( 8 - 2 = 6 \)[/tex] → Output is 5 (does not match)
- For input 7: [tex]\( 7 - 2 = 5 \)[/tex] → Output is 3 (does not match)
Since this rule does not produce the correct output for inputs 8 and 7, Rule (A) is not the correct rule.
### Rule (B): Multiply the input by 0. Then add 5 to the result to get the output.
Let's apply this rule to each input:
- For input 9: [tex]\( 9 \times 0 + 5 = 0 + 5 = 5 \)[/tex] → Output is 7 (does not match)
- For input 8: [tex]\( 8 \times 0 + 5 = 0 + 5 = 5 \)[/tex] → Output is 5 (matches)
- For input 7: [tex]\( 7 \times 0 + 5 = 0 + 5 = 5 \)[/tex] → Output is 3 (does not match)
Since this rule does not produce the correct output for inputs 9 and 7, Rule (B) is not the correct rule.
### Rule (C): Multiply the input by 2. Then subtract 11 from the result to get the output.
Let's apply this rule to each input:
- For input 9: [tex]\( 9 \times 2 - 11 = 18 - 11 = 7 \)[/tex] → Output is 7 (matches)
- For input 8: [tex]\( 8 \times 2 - 11 = 16 - 11 = 5 \)[/tex] → Output is 5 (matches)
- For input 7: [tex]\( 7 \times 2 - 11 = 14 - 11 = 3 \)[/tex] → Output is 3 (matches)
Since this rule produces the correct output for all input values given, Rule (C) is the correct rule.
Therefore, the rule that correctly describes the relationship between the input and output pairs in the table is:
(C) Multiply the input by 2. Then subtract 11 from the result to get the output.
