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Sketch a function that has the following properties: lim f(x) = 2 *4-2 f(-2) = -1 lim f(x) DNE *→0 The domain of f is (-∞0, 2) U (2,00)

Sketch a function that has the following properties: lim f(x) = 2 *4-2 f(-2) = -1 lim f(x) DNE *→0 The domain of f is (-∞0, 2) U (2,00)

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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**Sketch a Function with the Following Properties:** 1. \(\lim_{x \to 2} f(x) = 2\) 2. \(f(-2) = -1\) 3. \(\lim_{x \to 0} f(x)\) DNE The domain of \(f\) is \((-\infty, 2) \cup (2, \infty)\). --- **Graph Explanation:** Below is a grid for sketching the function. The x-axis ranges from -5 to 5, and the y-axis ranges from -5 to 5. Each line on the grid is spaced at intervals of 1. **Key Points to Consider:** - As \(x\) approaches 2 from the left or right, \(f(x)\) approaches 2, suggesting a point or horizontal line approaching but not crossing or including 2 at \(x=2\). - The point at \(x = -2\) is given by \(f(-2) = -1\). This is a specific point that should be clearly marked on the graph. - The limit as \(x\) approaches 0 does not exist, indicating a discontinuity or asymptote at \(x=0\). - The function is not defined exactly at \(x = 2\), and the domain is split into two intervals: all real numbers less than 2 or greater than 2. *Note: You may upload a picture of your graph if you'd prefer to make it by hand.*
Transcribed Image Text:**Sketch a Function with the Following Properties:** 1. \(\lim_{x \to 2} f(x) = 2\) 2. \(f(-2) = -1\) 3. \(\lim_{x \to 0} f(x)\) DNE The domain of \(f\) is \((-\infty, 2) \cup (2, \infty)\). --- **Graph Explanation:** Below is a grid for sketching the function. The x-axis ranges from -5 to 5, and the y-axis ranges from -5 to 5. Each line on the grid is spaced at intervals of 1. **Key Points to Consider:** - As \(x\) approaches 2 from the left or right, \(f(x)\) approaches 2, suggesting a point or horizontal line approaching but not crossing or including 2 at \(x=2\). - The point at \(x = -2\) is given by \(f(-2) = -1\). This is a specific point that should be clearly marked on the graph. - The limit as \(x\) approaches 0 does not exist, indicating a discontinuity or asymptote at \(x=0\). - The function is not defined exactly at \(x = 2\), and the domain is split into two intervals: all real numbers less than 2 or greater than 2. *Note: You may upload a picture of your graph if you'd prefer to make it by hand.*
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