Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Transcription for Educational Website:**
---
**Title:** Write an Equation for the Function Graphed Below
**Graph Description:**
The graph depicts a function with two vertical asymptotes and a rational function behavior. The vertical asymptotes are represented by red dashed lines at \(x = -2\) and \(x = 4\).
- The curve approaches these vertical lines but never touches them, indicating points where the function is undefined.
- The graph includes two main branches:
- For \(x < -2\), the graph approaches negative infinity as it moves leftward.
- Between \(x = -2\) and \(x = 4\), the graph decreases towards negative infinity as \(x\) approaches \(-2\) from the right, and it heads towards positive infinity as it approaches 4 from the left.
- For \(x > 4\), the graph increases from negative infinity and continues to increase slightly as it moves rightward.
**Prompt:**
y = [Equation goes here]
**Instructions:** Determine and write the equation that represents the function graphed above. The graph suggests a form of a rational function with the given asymptotes.
---
This layout is designed to facilitate understanding of the graph's features and assist in deriving the equation.](https://content.bartleby.com/qna-images/question/a7a9d0ad-fec9-4f0d-b494-c459fdb0f55b/ce5afe8d-88e2-4a77-a379-63d79a8153c1/xlla4t_processed.png)
Transcribed Image Text:**Transcription for Educational Website:**
---
**Title:** Write an Equation for the Function Graphed Below
**Graph Description:**
The graph depicts a function with two vertical asymptotes and a rational function behavior. The vertical asymptotes are represented by red dashed lines at \(x = -2\) and \(x = 4\).
- The curve approaches these vertical lines but never touches them, indicating points where the function is undefined.
- The graph includes two main branches:
- For \(x < -2\), the graph approaches negative infinity as it moves leftward.
- Between \(x = -2\) and \(x = 4\), the graph decreases towards negative infinity as \(x\) approaches \(-2\) from the right, and it heads towards positive infinity as it approaches 4 from the left.
- For \(x > 4\), the graph increases from negative infinity and continues to increase slightly as it moves rightward.
**Prompt:**
y = [Equation goes here]
**Instructions:** Determine and write the equation that represents the function graphed above. The graph suggests a form of a rational function with the given asymptotes.
---
This layout is designed to facilitate understanding of the graph's features and assist in deriving the equation.
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