Question

which relation is a function?
input output
0 1
0 2
1 3
1 4
input output
1 2
2 4
4 6
4 8
input output
2 6
2 5
6 4
6 3
input output
1 2
2 2
3 3
4 3

Explanation:

Step1: Recall function definition

A relation is a function if every input has exactly one output.

Step2: Check first table

Input 0 maps to 1 and 2; input 1 maps to 3 and 4. This violates the function rule.

Step3: Check second table

Input 4 maps to 6 and 8. This violates the function rule.

Step4: Check third table

Input 2 maps to 6 and 5; input 6 maps to 4 and 3. This violates the function rule.

Step5: Check fourth table

Input 1→2, 2→2, 3→3, 4→3. Every input has only one output. This satisfies the function rule.

Answer:

The bottommost table (Input: 1,2,3,4; Output:2,2,3,3)