Question

1. circle all the relations that are functions.

input output
0 → -5
0 → -4
1 → -4
2 → -3
3 → -2

x	y
-8	-1
-4	-1
0	-1
4	-1
8	-1

{(-5, 3), (-1, 0), (3, -4), (-1, 2)}

Explanation:

Step1: Recall the function definition

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

Step2: Analyze the first relation (mapping diagram)

• Input 0 is mapped to - 5 and - 4. So, one input has two outputs. Thus, this relation is not a function.

Step3: Analyze the second relation (table)

• For \(x=-8\), \(y = - 1\); for \(x=-4\), \(y=-1\); for \(x = 0\), \(y=-1\); for \(x = 4\), \(y=-1\); for \(x = 8\), \(y=-1\). Each \(x\) - value has exactly one \(y\) - value. So, this relation is a function.

Step4: Analyze the third relation (set of ordered pairs)

• The ordered pairs are \((-5,3),(-1,0),(3,-4),(-1,2)\). The input \(x=-1\) is mapped to \(y = 0\) and \(y = 2\). So, one input has two outputs. Thus, this relation is not a function.

Answer:

The relation represented by the table (with \(x\) values \(-8,-4,0,4,8\) and corresponding \(y=-1\) for each) is a function. So we circle the table - based relation.