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

Question

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

Answer 1

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.