Question
Mathematics
Which table represents a function?
 $x$x $y$y -1 -2 -1 -1 0 0 2 1 2 2
x y -1 -2 -1 -1 0 0 2 1 2 2
 $x$x $y$y -2 0 -1 1 0 1 -1 2 -2 2
x y -2 0 -1 1 0 1 -1 2 -2 2
 $x$x $y$y 2 -2 1 -1 0 0 1 1 2 2
x y 2 -2 1 -1 0 0 1 1 2 2
 $x$x $y$y -2 -1 -1 -1 0 0 1 1 2 2
x y -2 -1 -1 -1 0 0 1 1 2 2
A function is a set of ordered pairs in which no two ordered pairs have the same value of the first coordinate, but different values of the second coordinate. This means that for a given $x$x, there can only be one corresponding $y$y.
Out of the given tables, only the second table represents a function, because for each unique value of $x$x, there is only one corresponding value of $y$y.
In the other tables, there are repeated $x$x values with different corresponding $y$y values, which means they do not represent a function. Specifically, in the first table, there are two ordered pairs with $x=-1$x=-1 but different $y$y values. In the third and fourth tables, there are two ordered pairs with the same $x$x and different $y$y values.