four relations are shown below. click on the tabs to see them. relation 1 relation 2 relation 3 relation 4…

four relations are shown below. click on the tabs to see them. relation 1 relation 2 relation 3 relation 4 domain range j → r y → d h → h r → y d → j your answer check the box corresponding to each relation that represents a function. try one last time ☐ relation 2 ☐ relation 3 ☐ relation 4 ☐ none of the relations

four relations are shown below. click on the tabs to see them. relation 1 relation 2 relation 3 relation 4 domain range j → r y → d h → h r → y d → j your answer check the box corresponding to each relation that represents a function. try one last time ☐ relation 2 ☐ relation 3 ☐ relation 4 ☐ none of the relations

Answer

Explanation:

Step1: Recall Function Definition

A function is a relation where each element in the domain maps to exactly one element in the range. So, we check if any domain element has more than one range mapping.

Step2: Analyze Relation 2

  • Domain elements: ( j, y, h, r, d )
  • ( j \to r ), ( y \to d ), ( h \to h ), ( r \to y ), ( d \to j )
  • Each domain element has exactly one range element. So Relation 2 is a function? Wait, no—wait, wait, let's re - check. Wait, the domain elements: ( j ) maps to ( r ), ( y ) maps to ( d ), ( h ) maps to ( h ), ( r ) maps to ( y ), ( d ) maps to ( j ). Wait, but wait, is there any domain element with multiple mappings? No. Wait, but maybe I misread. Wait, no, in a function, each input (domain) has one output (range). So for Relation 2, each domain element has one range element. Wait, but maybe the original problem's Relation 2—wait, no, maybe I made a mistake. Wait, no, the key is: in a function, no two arrows come from the same domain element. Let's list domain elements: ( j ), ( y ), ( h ), ( r ), ( d ). Each has one arrow. So Relation 2 is a function? Wait, but the options—wait, the user's question is to check the box for each relation that is a function. But since we can only see Relation 2 here, but maybe in the original problem, Relation 2 is a function? Wait, no, wait, maybe I messed up. Wait, no, let's re - evaluate. Wait, the domain elements: ( j ) maps to ( r ), ( y ) maps to ( d ), ( h ) maps to ( h ), ( r ) maps to ( y ), ( d ) maps to ( j ). Each domain element has exactly one range element. So Relation 2 is a function. But wait, maybe the other relations (not shown) are not, but based on what's shown, Relation 2 is a function. Wait, but the user's question is to check the box. So the answer is to check the box for Relation 2? Wait, no, maybe I made a mistake. Wait, no, the definition of a function is that each element in the domain has exactly one image in the range. So for Relation 2, each domain element (( j, y, h, r, d )) has exactly one range element. So Relation 2 is a function.

Answer:

(\boxed{\text{Relation 2}}) (assuming that based on the analysis, Relation 2 is a function. If there were more relations, we would analyze them too, but with the given info, Relation 2 meets the function criteria as each domain element has one range mapping)