To determine whether the table represents a function, we need to check if each input \( x \) corresponds to exactly one output \( y \). In other words, for a relation to be a function, no two different pairs can have the same \( x \) value with different \( y \) values.
Looking at the table provided:
- For \( x = 2 \), \( y = 1 \)
- For \( x = 4 \), \( y = 3 \)
- For \( x = 6 \), \( y = 3 \)
- For \( x = 8 \), \( y = 4 \)
- For \( x = 10 \), \( y = 6 \)
We can see that:
- The inputs \( 2 \), \( 4 \), \( 6 \), \( 8 \), and \( 10 \) are all unique, meaning no \( x \) value is repeated in the pairs.
Even though \( y = 3 \) corresponds to both \( x = 4 \) and \( x = 6 \), this is acceptable in a function because the output \( y \) can be the same for different inputs \( x \).
Since each input has a unique output (or the same output for different inputs), this table represents a function.