Question

look at this mapping diagram:
domain
19
4
18
range
14
18
-14
is this relation a function?
yes
no

Explanation:

Step1: Recall function definition

A function is a relation where each element in the domain is mapped to exactly one element in the range.

Step2: Check domain elements

• Domain element 19: Mapped to 14 (one mapping).
• Domain element 4: Mapped to 18 and -14? Wait, no, looking at the diagram, 4 is mapped to 18 and another? Wait, no, the diagram: 19→14, 4→18 and 4→-14? Wait, no, let's re-examine. Wait, the domain has 19, 4, 18. Wait, 4 is connected to two range elements? Wait, no, the arrows: 19→14, 4→18 and 4→-14? Wait, no, the diagram: 19→14, 4→18, 4→-14? Wait, no, maybe I misread. Wait, the domain is {19, 4, 18}, range {14, 18, -14}. Wait, 4 is connected to two range elements? Wait, no, the arrows: 19→14, 4→18, 4→-14? Wait, no, maybe 4 is connected to 18 and 14? Wait, no, the green arrows: 19→14, 4→18, 4→-14? Wait, no, let's look again. The domain: 19, 4, 18. Range:14, 18, -14. Arrows: 19→14, 4→18, 4→-14? Wait, no, maybe 4 is connected to two range elements. Wait, the definition of a function: each domain element has exactly one range element. So if any domain element has more than one range element, it's not a function. So 4 is mapped to two range elements (since there are two arrows from 4), so that means the relation is not a function. Wait, no, maybe I misread the arrows. Wait, the diagram: 19→14, 4→18, 4→-14? Wait, no, maybe 4 is connected to 18 and 14? Wait, no, the arrows: 19→14, 4→18, 18→14? Wait, no, the domain element 18: where is it mapped? Wait, maybe I made a mistake. Wait, the domain has 19, 4, 18. Let's list all mappings:

• 19: maps to 14 (one arrow)
• 4: maps to 18 and -14? Wait, no, the arrows: 19→14, 4→18, 4→-14? Wait, no, the green arrows: 19→14, 4→18, 4→-14? Wait, no, maybe 4 is connected to two range elements. So since 4 (a domain element) is mapped to more than one range element, this relation is not a function.

Wait, no, maybe I misread. Wait, the domain is 19, 4, 18. Let's check each domain element:

• 19: only one arrow (to 14) → good.
• 4: two arrows (to 18 and to -14? Or to 18 and 14? Wait, the range is 14, 18, -14. The arrows: 19→14, 4→18, 4→-14? Wait, no, maybe 4 is connected to 18 and 14? Wait, the diagram: 19→14, 4→18, 4→14? No, the original diagram: let's see, the user's diagram: Domain {19,4,18}, Range {14,18,-14}. Arrows: 19→14, 4→18, 4→-14? Wait, no, maybe 4 is connected to two range elements. So by the definition of a function, each input (domain element) must have exactly one output (range element). So if 4 has two outputs, then it's not a function. Therefore, the answer is no.

Answer:

no