Question

four relations are shown below. click on the tabs to see them. relation 1 relation 2 relation 3 relation 4 domain range j pencil z cloud f pencil b cloud v pencil j cloud

Explanation:

Step1: Recall Function Definition

A function is a relation where each domain (input) has exactly one range (output). So we check each domain element.

Step2: Check Domain Elements

• Domain \( j \): Maps to "pencil" and "cloud" (two outputs).
• Domain \( z \): Maps to "cloud" (one output).
• Domain \( f \): Maps to "pencil" (one output).
• Domain \( b \): Maps to "cloud" (one output).

Since \( j \) has two outputs, this relation is not a function.

Answer:

This relation is not a function because the domain element \( j \) is mapped to two different range elements ("pencil" and "cloud").