Determining if a Relation is a Function or not
Answer:
1: Function
2: Not a Function
Step-by-step explanation:
We consider a Relation to be a Function if one input from the Domain corresponds to only one output from the Range or multiple inputs from the Domain corresponds to only one output from the Range.
Part 1:
Given:
[tex]&\text{Domain} &\text{Range} \\ &- 5 &8 \\ &-2 &-10 \\ &0 &8 \\ &6 &15[/tex]
We can see from the given table that there's no input from the Domain that corresponds to multiple outputs from the Range. We can only see multiple inputs, [tex]-5[/tex] and [tex]0[/tex] from the Domain that corresponds to only one same output from the Range, [tex]8[/tex]. So, we consider this relation a function.
Part 2:
Please refer to the image for the Given Graph.
If we consider [tex]x[/tex] to be Domain and [tex]y[/tex] to be Range, we can see for the same input, [tex]-4[/tex], it corresponds to infinite outputs. Other way of view this is that consider the point [tex](-4,n)[/tex], no matter what real values of the output, [tex]n[/tex], the point will still be on the line. So, this graph is not a function.
