Question

IV. Identifying Functions

Answer 1

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:

$&\text{Domain} &\text{Range} \\ &- 5 &8 \\ &-2 &-10 \\ &0 &8 \\ &6 &15$

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, $-5$ and $0$ from the Domain that corresponds to only one same output from the Range, $8$. So, we consider this relation a function.

Part 2:

Please refer to the image for the Given Graph.

If we consider $x$ to be Domain and $y$ to be Range, we can see for the same input, $-4$, it corresponds to infinite outputs. Other way of view this is that consider the point $(-4,n)$, no matter what real values of the output, $n$, the point will still be on the line. So, this graph is not a function.