VIPSolutionsgive answer in 2 step with explanation at the end of each step and final answer at the end. wr each relation, decide whether or not it is a functura. \ table [ [ , \ table [ [ Function ] , [ Not a function ] ] ] , [ Function Not a function ] , [ Relation 3 { ( h , z ) , ( w , h ) , ( e , h ) , ( z , z ) } , Relation 4 { ( 7 , n ) , ( 0 , n ) , ( 4 , n ) , ( - 3 , n ) }h Forno a TT ei Reser aod pin. Er E 7 pen Nl pi 3 . 8 A 4 om 9 3 paper =8 . O Function [ © uncon 0 Mot function | Oot tncton Tis Relations Relation 4 | Aenea) {G0 8.3.) O Function © uncon | O ota uncon © ota function Bs
Question:
give answer in 2 step with explanation at the end of each step and final answer at the end.
wr each relation, decide whether or not it is a functura.
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Function
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]
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Relation
3
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h Forno a TT ei
Reser aod pin.
Er E 7
pen Nl
pi 3 .
8 A 4
om 9 3
paper =8 .
O Function
[ © uncon 0 Mot function
| Oot tncton
Tis Relations Relation 4
| Aenea) {G0 8.3.)
O Function © uncon
| O ota uncon © ota function Bs
This is AI generated Response.
Asked by: Pagal
Created at: 2025-05-30 19:24:20
Asked by: Pagal
Created at: 2025-05-30 19:24:20
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Let's go through each relation step by step and decide if it is a function.
---
### **Relation 1**
#### **Step 1:** Check if each element in the **domain** maps to exactly one element in the **range**.
- Sky → 0
- Pen → 0
- Desk → 0
- Pencil → 0
- Paper → -9
Each domain value maps to only one range value.
#### **Step 2:** Decide if it's a function.
- **Explanation:** A function assigns each input (domain) to exactly one output (range). Here, no domain value is assigned to more than one range value.
- **Final Answer:** **Function**
---
### **Relation 2**
#### **Step 1:** Check if each element in the **domain** maps to exactly one element in the **range**.
- -9 → 7
- 0 → 0
- 4 → 0
- 9 → 3
Each domain value maps to only one range value.
#### **Step 2:** Decide if it's a function.
- **Explanation:** Even though two different domain values (0 and 4) map to the same range value (0), each input from the domain still maps to only one output.
- **Final Answer:** **Function**
---
### **Relation 3**
\(\{(h, z), (w, h), (e, h), (z, z)\}\)
#### **Step 1:** Check if each first element (domain) is unique.
- h → z
- w → h
- e → h
- z → z
All first elements (h, w, e, z) are unique.
#### **Step 2:** Decide if it's a function.
- **Explanation:** Each domain value is paired with only one range value.
- **Final Answer:** **Function**
---
### **Relation 4**
\(\{(7, n), (0, n), (4, n), (-3, n)\}\)
#### **Step 1:** Check if each first element (domain) is unique.
- 7 → n
- 0 → n
- 4 → n
- -3 → n
All domain values are unique.
#### **Step 2:** Decide if it's a function.
- **Explanation:** Each domain value maps to exactly one range value.
- **Final Answer:** **Function**
---
## **Summary of Answers**
1. **Relation 1:** Function
2. **Relation 2:** Function
3. **Relation 3:** Function
4. **Relation 4:** Function
---
**Note:** In all cases, each domain value is assigned to only one range value, so all are functions. Even if multiple domain values map to the same range value, it is still a function. It only fails to be a function if a single domain value maps to **more than one** range value.
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