Write an equation for the function graphed below 5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
**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.
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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