Question

determine if the following relationships represent functions:
2)

x	y
2	3
3	-2
3	5
5	1

3)

x	y
2	-1
5	3
6	0
9	2

Explanation:

Step1: Recall function definition

A relation is a function if each input ($x$-value) has exactly one output ($y$-value).

Step2: Analyze Relationship 2

Check $x$-values: $x=3$ maps to $y=-2$ and $y=5$.

Step3: Conclude for Relationship 2

Since one $x$ has two $y$s, it is not a function.

Step4: Analyze Relationship 3

Check $x$-values: Each $x$ ($-1,2,5,6,9$) maps to only one $y$.

Step5: Conclude for Relationship 3

All $x$s have unique $y$s, so it is a function.

Answer:

1. Relationship 2: Not a function
2. Relationship 3: Is a function