Question

Which of these relations are functions?

Answer 1

Answer:  None of them are functions.

Step-by-step explanation:

By definition, a relation is a function  if and only if each input value have an unique output value.

You need to remember that the input values are the x-values and the output values are the y-values.

In the first table you can observe that the input value 2 has two different output values:

$x=2;y=11\\\\x=2;y=15$

Therefore, this relation is not a function.

Notice that in the second table the input value -4 has two different output values:

$x=-4;y=-2\\\\x=-4;y=-5$

Therefore, this relation is not a function.

In the set $\{(-5,-7), (-2,-7), (7,17), (-5,21)\}$, observe that the input value -5 has two different output values:

$x=-5;y=-7\\\\x=-5;y=21$

Therefore, this relation is not a function.