Sketch the graph of the following functions, identifying relative max and mins, points of inflection, intercepts, and asymptotes. a. f(x) =
Sketch the graph of the following functions, identifying relative max and mins, points of inflection, intercepts, and asymptotes. a. f(x) =
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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![**Instructions for Graphing Functions**
**Objective:** Sketch the graph of the following functions, identifying the following features:
- Relative maxima and minima
- Points of inflection
- Intercepts
- Asymptotes
---
**Function a:**
\[ f(x) = \frac{1}{x+2} \]
- **Relative Maxima and Minima:** Identify any peaks or troughs in the curve.
- **Points of Inflection:** Determine where the curve changes concavity.
- **Intercepts:** Calculate where the graph intersects the x-axis and y-axis.
- **Asymptotes:** Determine the vertical and horizontal asymptotes.
---
**Function b:**
\[ f(x) = \frac{x-2}{x^2-1} \]
- **Relative Maxima and Minima:** Analyze the graph for any local peaks or troughs.
- **Points of Inflection:** Find any points where the curve changes its concavity.
- **Intercepts:** Locate intersections with the axes.
- **Asymptotes:** Identify vertical and horizontal asymptotes.
---
To sketch these graphs effectively, begin by analyzing each component systematically, using calculus techniques and testing function behavior at key points and intervals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37f6a860-f974-494c-9785-179491d557d0%2F39c78579-5498-4486-b3ec-9de6bb71e384%2F43e6f2_processed.png&w=3840&q=75)
Transcribed Image Text:**Instructions for Graphing Functions**
**Objective:** Sketch the graph of the following functions, identifying the following features:
- Relative maxima and minima
- Points of inflection
- Intercepts
- Asymptotes
---
**Function a:**
\[ f(x) = \frac{1}{x+2} \]
- **Relative Maxima and Minima:** Identify any peaks or troughs in the curve.
- **Points of Inflection:** Determine where the curve changes concavity.
- **Intercepts:** Calculate where the graph intersects the x-axis and y-axis.
- **Asymptotes:** Determine the vertical and horizontal asymptotes.
---
**Function b:**
\[ f(x) = \frac{x-2}{x^2-1} \]
- **Relative Maxima and Minima:** Analyze the graph for any local peaks or troughs.
- **Points of Inflection:** Find any points where the curve changes its concavity.
- **Intercepts:** Locate intersections with the axes.
- **Asymptotes:** Identify vertical and horizontal asymptotes.
---
To sketch these graphs effectively, begin by analyzing each component systematically, using calculus techniques and testing function behavior at key points and intervals.
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