Does this table represent a function? Why or why not?

x y
2 1
4 3
6 3
8 4
10 6

1 answer

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.