8. Consider the set f = {(x, y) E Z xZ:x+3y = 4}. Is this a function from Z to Z? Explain. %3D %3D

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ISBN:9780470458365
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Question 8 please 12.2

# Educational Text - Functions

## Exercises for Section 12.1

1. **Exercise 1**  
   Suppose \( A = \{0, 1, 2, 3, 4\}, B = \{2, 3, 4, 5\} \) and \( f = \{(0,3), (1,3), (2,4), (3,2), (4,2)\} \).  
   State the domain and range of \( f \). Find \( f(2) \) and \( f(1) \).

2. **Exercise 2**  
   Suppose \( A = \{a, b, c, d\}, B = \{2, 3, 4, 5, 6\} \) and \( f = \{(a,2), (b,3), (c,4), (d,5)\} \).  
   State the domain and range of \( f \). Find \( f(b) \) and \( f(d) \).

3. **Exercise 3**  
   There are four different functions \( f: \{a, b\} \rightarrow \{0, 1\} \).  
   List them. Diagrams suffice.

4. **Exercise 4**  
   There are eight different functions \( f: \{a, b, c\} \rightarrow \{0, 1\} \).  
   List them. Diagrams suffice.

5. **Exercise 5**  
   Give an example of a relation from \( \{a, b, c, d\} \) to \( \{d, e\} \) that is not a function.

6. **Exercise 6** (Highlighted)  
   Suppose \( f: \mathbb{Z} \rightarrow \mathbb{Z} \) is defined as \( f = \{(x, 4x + 5) : x \in \mathbb{Z}\} \).  
   State the domain, codomain, and range of \( f \). Find \( f(10) \).

7. **Exercise 7**  
   Consider the set \( f = \{(x, y) \in \mathbb{Z} \times \mathbb{Z} : 3x + y = 4\}
Transcribed Image Text:# Educational Text - Functions ## Exercises for Section 12.1 1. **Exercise 1** Suppose \( A = \{0, 1, 2, 3, 4\}, B = \{2, 3, 4, 5\} \) and \( f = \{(0,3), (1,3), (2,4), (3,2), (4,2)\} \). State the domain and range of \( f \). Find \( f(2) \) and \( f(1) \). 2. **Exercise 2** Suppose \( A = \{a, b, c, d\}, B = \{2, 3, 4, 5, 6\} \) and \( f = \{(a,2), (b,3), (c,4), (d,5)\} \). State the domain and range of \( f \). Find \( f(b) \) and \( f(d) \). 3. **Exercise 3** There are four different functions \( f: \{a, b\} \rightarrow \{0, 1\} \). List them. Diagrams suffice. 4. **Exercise 4** There are eight different functions \( f: \{a, b, c\} \rightarrow \{0, 1\} \). List them. Diagrams suffice. 5. **Exercise 5** Give an example of a relation from \( \{a, b, c, d\} \) to \( \{d, e\} \) that is not a function. 6. **Exercise 6** (Highlighted) Suppose \( f: \mathbb{Z} \rightarrow \mathbb{Z} \) is defined as \( f = \{(x, 4x + 5) : x \in \mathbb{Z}\} \). State the domain, codomain, and range of \( f \). Find \( f(10) \). 7. **Exercise 7** Consider the set \( f = \{(x, y) \in \mathbb{Z} \times \mathbb{Z} : 3x + y = 4\}
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