Question

look at this mapping diagram:
domain: -13, 12, 18, 17
range: 18, 8
is this relation a function?
options: yes, no

Explanation:

Step1: Recall the definition of a function

A function is a relation where each element in the domain is paired with exactly one element in the range.

Step2: Analyze the domain elements

• The domain element \(-13\): Let's check its mappings. From the diagram, \(-13\) maps to \(18\) (one mapping).
• The domain element \(12\): Check its mappings. It has multiple mappings (to both \(18\) and \(8\)? Wait, no, looking at the diagram, actually, let's re - examine. Wait, the domain has \(-13\), \(12\), \(18\), \(17\). Wait, the element \(18\) in the domain: how many times is it mapped? Wait, no, the key is each domain element must have only one range element. Wait, looking at the domain element \(12\): does it map to more than one? Wait, the diagram: \(-13\) maps to \(18\), \(12\) maps to... Wait, no, the problem is: let's list the domain elements: \(-13\), \(12\), \(18\), \(17\). Now, check if any domain element is mapped to more than one range element. Wait, the element \(18\) in the domain: how many arrows? Wait, no, wait the domain element \(12\): does it have multiple arrows? Wait, the diagram shows that the domain element \(18\) (wait, no, the domain is \(-13\), \(12\), \(18\), \(17\)). Wait, the element \(18\) in the domain: how many range elements is it mapped to? Wait, no, actually, the mistake is: in a function, each input (domain element) has exactly one output (range element). So we need to check each domain element:
• \(-13\): Let's see the arrows. It maps to \(18\) (one arrow).
• \(12\): How many arrows? From the diagram, it looks like \(12\) is mapped to more than one range element (maybe \(18\) and \(8\)? Wait, no, the diagram: let's look again. The domain is \(-13\), \(12\), \(18\), \(17\). The range is \(18\), \(8\). Now, the element \(18\) in the domain: how many times is it mapped? Wait, no, the element \(12\): does it have two arrows? Wait, the diagram shows that the domain element \(18\) (wait, no, the domain element \(12\)): actually, the problem is that the domain element \(18\) (wait, no, the domain is \(-13\), \(12\), \(18\), \(17\)). Wait, the key is: for a relation to be a function, every element in the domain must have exactly one corresponding element in the range. So if any domain element is paired with more than one range element, it's not a function. Looking at the domain element \(18\) (wait, no, the domain element \(12\)): Wait, maybe I misread. Let's check the domain element \(18\) (the one in the domain). How many arrows does it have? It has multiple arrows (mapped to more than one range element). Wait, no, the domain element \(12\): does it have multiple arrows? Wait, the diagram: the domain is \(-13\), \(12\), \(18\), \(17\). The element \(18\) in the domain: let's count the arrows from \(18\). It has more than one arrow, meaning it is mapped to more than one range element. Also, the element \(12\): maybe it is also mapped to more than one? Wait, the definition of a function is that each input has exactly one output. So if any input (domain element) has more than one output (range element), it's not a function. So in this mapping, at least one domain element (like \(18\) or \(12\)) is mapped to more than one range element. So the relation is not a function.

Answer:

no