Select ALL the correct answers.
Which of these relations are functions?
Two ellipses labeled x and y. 4 in x corresponds to 21 in y. 6 in x corresponds to negative 7 in y. 3 in x corresponds to negative 23 in y. Negative 5 in x corresponds to 12 in y.
A parabola declines from (negative 2, 5) through (1, negative 4) and rises through (4, 5) on the x y coordinate plane.

x 4 -4 7 -7 -4
y 3 -2 11 5 -5
{(-5,-7), (-2,-7), (7,17), (-5,21)}
A graph plots six points at (negative 5, 5), (negative 4, negative 4), (1, negative 1), (1, 1), (3, 3), and (5, 4) on the x y coordinate plane.

x 2 -2 6 2 -6
y 11 -5 21 15 -15

To determine which of these relations are functions, we need to check if each input value (x-value) corresponds to exactly one output value (y-value). Let's analyze each relation:

Two ellipses labeled x and y:

4 in x corresponds to 21 in y

6 in x corresponds to -7 in y

3 in x corresponds to -23 in y

-5 in x corresponds to 12 in y

This relation is not a function because for the x-values -5 and 6, there are two different y-values.

A parabola declining and then rising:

It starts at (-2, 5), goes through (1, -4), and rises to (4, 5).

This relation is a function because each x-value corresponds to exactly one y-value.

Points plotted on a graph:

(-5, -7), (-2, -7), (7, 17), (-5, 21)

This relation is not a function because for the x-value -5, there are two different y-values.

Six points plotted on a graph:

(-5, 5), (-4, -4), (1, -1), (1, 1), (3, 3), (5, 4)

This relation is not a function because for the x-value 1, there are two different y-values.

So, out of the given options, only the parabola declining and then rising is a function.