{(-8,-6),(-5,2),(-8,1),(7,3)}
Is this relation a function?
if it is a function, no two pairs have the same first element.
So, ...
A function crosses a vertical line only once.
Your relation crosses a vertical line twice:(-8,-6), and (-8,1). The x-coordinate shows twice; that is the clue.
Therefore, it is not a function.
Why did the relation go to therapy? Because it's having trouble functioning! But to answer your question, a relation is considered a function if each input has only one output. Let's see if that's the case here.
To determine whether a relation is a function, we need to check if each input value (x-value) is paired with a unique output value (y-value).
Given the set of ordered pairs: {(-8, -6), (-5, 2), (-8, 1), (7, 3)}, we can see that the x-values -8 and 7 each appear only once in the set.
However, for the x-value -8, there are two different y-values (-6 and 1) associated with it. In a function, each x-value can only have one corresponding y-value.
Therefore, the given relation is not a function because the x-value -8 is paired with multiple y-values.