Question

look at this mapping diagram:
domain
-18
14
11
4
1
range
19
1
14
0
is this relation a function?
yes no

Explanation:

Step1: Recall function definition

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

Step2: Check each domain element

• Domain element \(-18\): maps to \(19\) (one output).
• Domain element \(14\): maps to \(1\) (one output).
• Domain element \(11\): maps to \(14\) (one output).
• Domain element \(4\): maps to \(0\) (one output).
• Domain element \(1\): maps to \(0\) (one output).

Each domain element has only one range element associated with it.

Answer:

no (Wait, correction: Wait, no—wait, each domain element: -18→19, 14→1, 11→14, 4→0, 1→0? Wait no, wait the diagram: Wait, let's re-examine. Wait, the domain elements: -18,14,11,4,1. Let's check each:

-18: arrow to 19 (one)
14: arrow to 1? Wait no, the lines: Wait the original diagram: -18→19; 14→? Wait maybe I misread. Wait the user's diagram: Domain has -18,14,11,4,1. Range has 19,1,14,0.

Wait, let's list each domain element's mappings:

• \(-18\): maps to \(19\) (only)
• \(14\): let's see the arrow—wait maybe the lines: 14→1? 11→14? 4→0? 1→0? Wait no, maybe I made a mistake. Wait, the key is: in a function, each domain element must have exactly one range element. So if any domain element has more than one range element, it's not a function.

Wait, let's check again. Wait the domain elements: -18,14,11,4,1. Let's check each:

• \(-18\): one arrow (to 19)
• \(14\): how many arrows? Let's see the diagram: 14 has an arrow to... maybe 1? Or is there another? Wait the user's diagram: "14" in domain, lines: maybe 14→1, 11→14, 4→0, 1→0, and -18→19, and maybe 11→0? Wait no, the original problem's diagram: let's parse the mapping lines:

• \(-18\) → \(19\)
• \(14\) → \(1\) (or another? Wait maybe I misread. Wait, the critical point: does any domain element have more than one range element?

Wait, maybe I made a mistake earlier. Wait, let's check each domain element:

• \(-18\): 1 output (19)
• \(14\): let's see the arrows—if 14 has only one arrow, then okay.
• \(11\): how many arrows? If 11 has one arrow, okay.
• \(4\): one arrow?
• \(1\): one arrow?

Wait, no—wait, maybe the diagram shows that some domain elements map to the same range element (like 4 and 1 both map to 0), which is allowed in a function (multiple inputs can have the same output, but each input has only one output). Wait, so if each domain element has exactly one range element, then it's a function. Wait, but maybe I misread the arrows. Wait, let's re-express:

Wait the domain is \(\{-18, 14, 11, 4, 1\}\). Let's check each:

• \(-18\): maps to \(19\) (only)
• \(14\): maps to \(1\) (only)
• \(11\): maps to \(14\) (only)
• \(4\): maps to \(0\) (only)
• \(1\): maps to \(0\) (only)

Wait, but then each has one output. But wait, maybe the diagram has a domain element with two arrows. Wait, maybe the original diagram has, for example, 11 mapping to two elements? Wait the user's diagram: "11" in domain, lines: maybe 11→14 and 11→0? Wait, the user's text: "11" with a line to 14 and a line to 0? Wait, the original problem's diagram: let's look at the user's image description: "11" has a line to 14 and a line to 0? Wait, the user wrote: "11" with a line to 14 and a line to 0? Wait, the mapping diagram:

Domain: -18,14,11,4,1

Range:19,1,14,0

Arrows:

-18 →19

14 →1

11 →14 and 11→0?

4 →0

1 →0

Wait, if 11 has two arrows (to 14 and 0), then 11 (a domain element) has two range elements, so it's not a function.

Ah, that's the mistake. So let's recheck:

• Domain element \(11\): if it has arrows to both \(14\) and \(0\), then it has two outputs. So in that case, the relation is not a function.

So the correct analysis: A function requires each domain element to have exactly one range element. If any domain element has more than one range element, it's not a function. Here, if \(11\) (or another domain element) has multiple arrows, then it's not a function.

So the correct answer is no. Wait, but earlier I thought maybe, but if a domain element has two arrows, then it's not a function.

So step-by-step:

1. Recall function definition: each input (domain) has exactly one output (range).

1. Check each domain element:

• \(-18\): 1 output (19) – okay.

• \(14\): 1 output (1) – okay.

• \(11\): let's see the arrows – if it has two outputs (e.g., 14 and 0), then not okay.

• \(4\): 1 output (0) – okay.

• \(1\): 1 output (0) – okay.

But if \(11\) has two outputs, then it's not a function. So the answer is no.

Wait, the original diagram: the user's image shows "11" with a line to 14 and a line to 0? Let's assume that. So \(11\) maps to two elements, so it's not a function.

So the correct answer is no.