To find the correct expression that translates the input values [tex]\( y \)[/tex] into the corresponding output values provided in the table, we need to analyze the relationship between each pair of input and output.
Here’s the table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Input } (y) & \text{Output} \\
\hline
34 & 37 \\
\hline
35 & 38 \\
\hline
36 & 39 \\
\hline
37 & 40 \\
\hline
\end{array}
\][/tex]
Let's analyze the relationship step-by-step:
1. Consider the first pair (34, 37):
To transform the input [tex]\( y = 34 \)[/tex] to the output 37, one option is to add 3:
[tex]\[
34 + 3 = 37
\][/tex]
2. Consider the second pair (35, 38):
To transform the input [tex]\( y = 35 \)[/tex] to the output 38, we again add 3:
[tex]\[
35 + 3 = 38
\][/tex]
3. Consider the third pair (36, 39):
Similarly, to transform the input [tex]\( y = 36 \)[/tex] to the output 39, we add 3:
[tex]\[
36 + 3 = 39
\][/tex]
4. Consider the fourth pair (37, 40):
Lastly, to transform the input [tex]\( y = 37 \)[/tex] to the output 40, we add 3:
[tex]\[
37 + 3 = 40
\][/tex]
From all these pairs, it's clear that the output is always the input [tex]\( y \)[/tex] plus 3.
Therefore, the expression that can be used to find the output numbers in the table is:
[tex]\[
\boxed{y + 3}
\][/tex]
This corresponds to option C.
