which table represents a function?

Answer:

The second table (top - right) represents a function.

Explanation:

Step1: Recall function definition

A function has one - to - one or many - to - one mapping, i.e., for each input $x$ there is exactly one output $y$.

Step2: Analyze first table

In the first table, when $x = 1$ and $x = 2$, there are multiple $y$ - values for the same $x$ values, so it's not a function.

Step3: Analyze second table

In the second table, for every unique $x$ value ($-2,-1,0,1,2$), there is a single, unique $y$ value. So it is a function.

Step4: Analyze third table

In the third table, when $x=-2$ and $x = - 1$, there are multiple $y$ - values for the same $x$ values, so it's not a function.

Step5: Analyze fourth table

In the fourth table, when $x=-1$ and $x = 2$, there are multiple $y$ - values for the same $x$ values, so it's not a function.