Graph one period of the equation below by first adjusting the vertical asymptotes, then adjust the key point based on the stretch or compression. y = 4 tan(2x)
Graph one period of the equation below by first adjusting the vertical asymptotes, then adjust the key point based on the stretch or compression. y = 4 tan(2x)
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
Please answer and graph it clearly so I can understand the graph please??
![**Instructions:**
Graph one period of the equation below by first adjusting the vertical asymptotes, then adjust the key point based on the stretch or compression.
\[ y = 4 \tan(2x) \]
**Provide your answer below:**
---
**Graph Explanation:**
- The graph shows the curve for the function \( y = 4 \tan(2x) \).
- **Vertical Asymptotes:** These are represented by the dashed lines at \( x = -\frac{\pi}{4} \) and \( x = \frac{\pi}{4} \). They indicate the points where the function is undefined.
- **Key Points:**
- The graph passes through several key points: \( (-\frac{\pi}{4}, 0) \), \( (\frac{\pi}{8}, 3) \), and \( (\frac{\pi}{4}, 0) \).
- These points are marked by black dots on the graph.
- **Curve Characteristics:**
- The red curve represents one period of the tangent function stretched vertically by a factor of 4.
- The period of the tangent curve is halved due to the `2x` inside the tangent function, resulting in periodicity between the vertical asymptotes.
**Note:** Use the graph to understand how the adjustment of parameters affects the shape and positioning of the tangent function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24f7b9fc-b934-4e37-ae35-bdc4b8c3050d%2Fbf7837dd-1d48-4035-84f6-4e92f2440959%2Fj7dq33b_processed.png&w=3840&q=75)
Transcribed Image Text:**Instructions:**
Graph one period of the equation below by first adjusting the vertical asymptotes, then adjust the key point based on the stretch or compression.
\[ y = 4 \tan(2x) \]
**Provide your answer below:**
---
**Graph Explanation:**
- The graph shows the curve for the function \( y = 4 \tan(2x) \).
- **Vertical Asymptotes:** These are represented by the dashed lines at \( x = -\frac{\pi}{4} \) and \( x = \frac{\pi}{4} \). They indicate the points where the function is undefined.
- **Key Points:**
- The graph passes through several key points: \( (-\frac{\pi}{4}, 0) \), \( (\frac{\pi}{8}, 3) \), and \( (\frac{\pi}{4}, 0) \).
- These points are marked by black dots on the graph.
- **Curve Characteristics:**
- The red curve represents one period of the tangent function stretched vertically by a factor of 4.
- The period of the tangent curve is halved due to the `2x` inside the tangent function, resulting in periodicity between the vertical asymptotes.
**Note:** Use the graph to understand how the adjustment of parameters affects the shape and positioning of the tangent function.
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