Question

four relations are shown below. click on the tabs to see them. relation 1 relation 2 relation 3 relation 4 domain range leaf paper 6 rock tree lake 1 check the box corresponding to each relation that represents a function. relation 1 relation 2 relation 3 relation 4 none of the relations

Explanation:

Step1: Recall the definition of a function

A relation is a function if every element in the domain is mapped to exactly one element in the range. That is, no two different arrows start from the same domain element.

Step2: Analyze Relation 1

In Relation 1, the domain elements are "leaf", "paper", "rock", "tree", "lake".

• "leaf" maps to 6.
• "paper" maps to 6.
• "rock" maps to 6.
• "tree" maps to 6.
• "lake" maps to 1.

Each domain element (leaf, paper, rock, tree, lake) is mapped to only one range element (either 6 or 1). There is no domain element that has more than one arrow (i.e., no domain element is mapped to more than one range element). So, Relation 1 satisfies the definition of a function.

(Note: Since we only have the details for Relation 1 here, assuming the other relations (if we had their details) might or might not be functions, but based on the given Relation 1, it is a function. However, since the problem shows tabs for other relations but we only have Relation 1's diagram, but from the given Relation 1, we can conclude it is a function. If we assume we need to check Relation 1: )

Answer:

Relation 1 (the box corresponding to Relation 1 should be checked as it is a function since each domain element has exactly one range element)