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Let N = {-2,–1,0,1, 2}. Define a function s: N → N by s(n) = n². Represent this function with a directed graph. %3D

Let N = {-2,–1,0,1, 2}. Define a function s: N → N by s(n) = n². Represent this function with a directed graph. %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please show all clear steps and explanation. (discrete mathematics)

**Problem 4:** Let \( N = \{-2, -1, 0, 1, 2\} \). Define a function \( s: N \to N \) by \( s(n) = n^2 \). Represent this function with a directed graph. **Detailed Explanation on Creating a Directed Graph:** 1. **Function Definition:** - The set \( N \) consists of the elements \(-2, -1, 0, 1, 2\). - The function \( s(n) = n^2 \) will map each element of \( N \) to its square. 2. **Mapping Elements:** - \( s(-2) = (-2)^2 = 4 \) - \( s(-1) = (-1)^2 = 1 \) - \( s(0) = 0^2 = 0 \) - \( s(1) = 1^2 = 1 \) - \( s(2) = 2^2 = 4 \) 3. **Directed Graph Representation** - Create nodes for each element in the set \( N \): \(-2, -1, 0, 1, 2\). - Create additional nodes for results that are not already included in \( N \), like \( 4 \). - Draw directed edges (arrows) from each element \( n \) to its mapped value \( s(n) \). - For instance, an arrow from node \(-2\) to node \(4\), and another from node \(2\) to node \(4\). - Connect node \(-1\) to node \(1\), node \(0\) to node \(0\), and node \(1\) to node \(1\). This graph visually represents the function \( s(n) = n^2 \) by showing how each input from the set \( N \) maps to its corresponding output.
Transcribed Image Text:**Problem 4:** Let \( N = \{-2, -1, 0, 1, 2\} \). Define a function \( s: N \to N \) by \( s(n) = n^2 \). Represent this function with a directed graph. **Detailed Explanation on Creating a Directed Graph:** 1. **Function Definition:** - The set \( N \) consists of the elements \(-2, -1, 0, 1, 2\). - The function \( s(n) = n^2 \) will map each element of \( N \) to its square. 2. **Mapping Elements:** - \( s(-2) = (-2)^2 = 4 \) - \( s(-1) = (-1)^2 = 1 \) - \( s(0) = 0^2 = 0 \) - \( s(1) = 1^2 = 1 \) - \( s(2) = 2^2 = 4 \) 3. **Directed Graph Representation** - Create nodes for each element in the set \( N \): \(-2, -1, 0, 1, 2\). - Create additional nodes for results that are not already included in \( N \), like \( 4 \). - Draw directed edges (arrows) from each element \( n \) to its mapped value \( s(n) \). - For instance, an arrow from node \(-2\) to node \(4\), and another from node \(2\) to node \(4\). - Connect node \(-1\) to node \(1\), node \(0\) to node \(0\), and node \(1\) to node \(1\). This graph visually represents the function \( s(n) = n^2 \) by showing how each input from the set \( N \) maps to its corresponding output.
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