Question

look at this mapping diagram:
domain
10
6
-7
-14
range
6
12
-6
16
is this relation a function?
yes
no

Explanation:

Step1: Recall function definition

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

Step2: Check domain elements

• Domain element 10: Let's see its mappings (but from diagram, check each domain element's number of outputs). Wait, domain elements: 10, 6, -7, -14. Wait, no—wait the domain has 10, 6, -7, -14? Wait no, looking at the diagram: the domain has 10, 6, -7, -14? Wait no, the domain box has 10, 6, -7, -14? Wait no, the domain is {10, 6, -7, -14}? Wait no, wait the domain elements: 10, 6, -7, -14? Wait, but wait the element 6 in domain: how many arrows? Let's check each domain element:

• 10: How many arrows? Wait the diagram: 10 has an arrow? Wait no, let's re-examine. Wait the domain is [10, 6, -7, -14], range [6,12,-6,16]. Now, check each domain element:

• 10: How many outputs? Let's see the arrows. Wait the green arrows: 10—wait maybe I misread. Wait no, the key is: in a function, each domain element must map to exactly one range element. So check if any domain element has more than one arrow (i.e., more than one range element).

Looking at the domain element 6: how many arrows? From the diagram, 6 in domain has multiple arrows? Wait the problem: the mapping diagram—let's see: domain elements are 10, 6, -7, -14. Wait, the domain element 6: does it have more than one arrow (i.e., map to more than one range element)? Let's check: if 6 in domain is connected to multiple range elements, then it's not a function.

Wait, the definition of a function: a relation where each input (domain) has exactly one output (range). So if any domain element has two or more range elements, it's not a function.

Looking at the diagram: let's list the domain elements and their mappings:

• 10: Let's see the arrows. Wait maybe the domain element 6: how many arrows? Let's check the diagram again. The domain has 10, 6, -7, -14. The range has 6,12,-6,16. Now, the element 6 in the domain: does it have more than one arrow (i.e., map to multiple range elements)? From the diagram, the element 6 in domain has at least two arrows (since there are multiple green arrows from 6 to range elements). Wait, so 6 (domain) maps to more than one range element. Therefore, since a domain element (6) has more than one output, this relation is not a function.

Wait, let's confirm:

Domain elements: 10, 6, -7, -14.

• 10: Let's see its mapping (but maybe 10 has one, 6 has multiple). Wait, the key is: if any domain element has two or more range elements, it's not a function. So in the diagram, the domain element 6 (the number 6 in domain) has more than one arrow (i.e., maps to more than one range value), so it's not a function.

Answer:

no