Sketch a graph of the curve y = g(x) from x = -5 to x = 5. Points (2, 3) and (4, 0) are on the graph of the function; the function has origin symmetry. You are given the following information. x = 13 are asymptotes; g(x) < O if x > 3; g'(x) = 0 9'(x) < 0 g'(x) > 0 if |x| < 2 if x = 12 or 14 if 2 < Ix| < 3
Sketch a graph of the curve y = g(x) from x = -5 to x = 5. Points (2, 3) and (4, 0) are on the graph of the function; the function has origin symmetry. You are given the following information. x = 13 are asymptotes; g(x) < O if x > 3; g'(x) = 0 9'(x) < 0 g'(x) > 0 if |x| < 2 if x = 12 or 14 if 2 < Ix| < 3
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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Transcribed Image Text:**Sketch a Graph of the Curve \( y = g(x) \)**
**Range:** \( x = -5 \) to \( x = 5 \).
**Points on the Graph:** (2, 3) and (4, 0).
**Function Attributes:**
- The function has origin symmetry.
- Vertical asymptotes at \( x = \pm3 \).
**Function Behavior:**
- \( g'(x) > 0 \) if \( |x| < 2 \).
- \( g'(x) = 0 \) if \( x = \pm2 \) or \( \pm4 \).
- \( g'(x) < 0 \) if \( 2 < |x| < 3 \).
**Graph Details:**
- **Graph 1:** Displays the function decreasing between \( x = -5 \) to \( -4 \), increasing from \( x = -2 \) to \( 2 \), and decreasing from \( x = 3 \) to \( 5 \) with asymptotes at \( x = \pm3 \).
- **Graph 2:** Shows similar structure but the increase and decrease patterns are shifted, maintaining origin symmetry.
- **Graph 3:** Features function with possible additional oscillations maintaining the given points and asymptotic behavior.
- **Graph 4:** Depicts variations in local maxima and minima and the asymptotic behavior around \( x = \pm3 \), adhering to the symmetry.
Each graph represents different ways \( g(x) \) can fulfill the provided conditions and symmetry characteristics.
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