### Exercise: Graph of $ f(x) = \cot(x) + 1 $#### Instructions:1. **Draw asymptotes as dashed lines on graph.**2. **Amplitude:** (Leave blank, as cotangent functions do not have an amplitude). 3. **Period:** $ 0 < Bx - C < \pi $ $ \_\_\_\_ < x < \_\_\_\_\_ $ (Fill in the blank intervals).4. **Domain:** All real numbers except every \_\_\_\_ (period), beginning at \_\_\_\_. 5. **Vertical shift:** (Leave blank, no vertical shift for this function).6. **Asymptotes:** $ x = \_\_\_\_\_, x = \_\_\_\_\_ $ (Identify the vertical asymptotes for one period).7. **Point of inflection:** $( \_\_\_\_\_, \_\_\_\_\_ )$ (Identify if exists).8. **1/4 and 3/4 points:** $( \_\_\_\_\_, \_\_\_\_\_ )$ and $( \_\_\_\_\_, \_\_\_\_\_ )$ (Mark these points on the graph).9. **Range:** $\_\_\_\_\_\_\_) (Define the range of the function).10. **Graph two periods of the curve. Draw the asymptotes as dashed lines.**#### Graph Description:The provided graph shows the \(y$-axis in the vertical direction and the $x$-axis in the horizontal direction. The x-values range from $-\pi$ to $2\pi$, and y-values range from $-3$ to $4$. Dashed vertical lines indicate the asymptotes where the function is undefined. Points are marked on the curve at regular intervals.Key points to include:- Vertical asymptotes at $ x = 0 $, $ x = \pi $, $ x = 2\pi $, etc.- Increasing behavior of the function $ f(x) $ within each period $(0, \pi)$ and $(\pi, 2\pi)$.- The function values transition smoothly through the points marked on the graph.Feel

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Answered: 3. Graph f(x) = cot x + 1 Draw…

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3. Graph f(x) = cot x + 1 Draw asymptotes as dashed lines on graph. %3D Amplitude = Period = 0 < Bx -C

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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Question

### Exercise: Graph of $ f(x) = \cot(x) + 1 $

#### Instructions:
1. **Draw asymptotes as dashed lines on graph.**

2. **Amplitude:**
(Leave blank, as cotangent functions do not have an amplitude).

3. **Period:**
$ 0 < Bx - C < \pi $
$ \_\_\_\_ < x < \_\_\_\_\_ $ (Fill in the blank intervals).

4. **Domain:**
All real numbers except every \_\_\_\_ (period), beginning at \_\_\_\_.

5. **Vertical shift:**
(Leave blank, no vertical shift for this function).

6. **Asymptotes:**
$ x = \_\_\_\_\_, x = \_\_\_\_\_ $ (Identify the vertical asymptotes for one period).

7. **Point of inflection:**
$( \_\_\_\_\_, \_\_\_\_\_ )$ (Identify if exists).

8. **1/4 and 3/4 points:**
$( \_\_\_\_\_, \_\_\_\_\_ )$ and $( \_\_\_\_\_, \_\_\_\_\_ )$ (Mark these points on the graph).

9. **Range:**
$\_\_\_\_\_\_\_) (Define the range of the function).

10. **Graph two periods of the curve. Draw the asymptotes as dashed lines.**

#### Graph Description:
The provided graph shows the \(y$-axis in the vertical direction and the $x$-axis in the horizontal direction. The x-values range from $-\pi$ to $2\pi$, and y-values range from $-3$ to $4$. Dashed vertical lines indicate the asymptotes where the function is undefined. Points are marked on the curve at regular intervals.

Key points to include:
- Vertical asymptotes at $ x = 0 $, $ x = \pi $, $ x = 2\pi $, etc.
- Increasing behavior of the function $ f(x) $ within each period $(0, \pi)$ and $(\pi, 2\pi)$.
- The function values transition smoothly through the points marked on the graph.

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