Write an equation for the function graphed below 5 4 2 1 - + + -7 -6 -5 -4 -3 -2 -1 1 2 4 5 6 7 -2 -3 -4 -5+ y = 3.
Write an equation for the function graphed below 5 4 2 1 - + + -7 -6 -5 -4 -3 -2 -1 1 2 4 5 6 7 -2 -3 -4 -5+ y = 3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Write an equation for the function graphed below.
![## Function Analysis
**Task:** Write an equation for the function graphed below.
### Description of the Graph
The graph displays a rational function with the following features:
1. **Vertical Asymptotes:** The graph has vertical asymptotes at \( x = -3 \) and \( x = 3 \), marked by red dashed lines. These are the values where the function is undefined, causing the graph to shoot up or down towards infinity.
2. **Horizontal Asymptote:** The graph approaches a horizontal asymptote as \( y = 0 \). This indicates that as \( x \) moves towards positive or negative infinity, the function values approach zero.
3. **Behavior of the Function:**
- As \( x \) approaches \(-3\) from the left, the function decreases towards negative infinity.
- As \( x \) approaches \(-3\) from the right, the function increases towards positive infinity.
- As \( x \) approaches \(3\) from the left, the function increases towards positive infinity.
- As \( x \) approaches \(3\) from the right, the function decreases towards negative infinity.
### Equation Form
The function's equation is likely of the form:
\[ y = \frac{a}{(x+3)(x-3)} \]
Where \( a \) is a constant. This form reflects the vertical asymptotes at \( x = -3 \) and \( x = 3 \), and the horizontal asymptote at \( y = 0 \). Adjust the value of \( a \) to fit other possible conditions or points on the graph not explicitly labeled here.
### Equation Input
**y =** [Enter your equation here based on the analysis above.]
This exercise helps in understanding the relationship between equations of rational functions and their graphical representations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F115f2332-4935-4bad-af45-155b63580edd%2Fd7a77785-e981-46d0-8fe6-4cce72ccb7b6%2F17x1qdi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Function Analysis
**Task:** Write an equation for the function graphed below.
### Description of the Graph
The graph displays a rational function with the following features:
1. **Vertical Asymptotes:** The graph has vertical asymptotes at \( x = -3 \) and \( x = 3 \), marked by red dashed lines. These are the values where the function is undefined, causing the graph to shoot up or down towards infinity.
2. **Horizontal Asymptote:** The graph approaches a horizontal asymptote as \( y = 0 \). This indicates that as \( x \) moves towards positive or negative infinity, the function values approach zero.
3. **Behavior of the Function:**
- As \( x \) approaches \(-3\) from the left, the function decreases towards negative infinity.
- As \( x \) approaches \(-3\) from the right, the function increases towards positive infinity.
- As \( x \) approaches \(3\) from the left, the function increases towards positive infinity.
- As \( x \) approaches \(3\) from the right, the function decreases towards negative infinity.
### Equation Form
The function's equation is likely of the form:
\[ y = \frac{a}{(x+3)(x-3)} \]
Where \( a \) is a constant. This form reflects the vertical asymptotes at \( x = -3 \) and \( x = 3 \), and the horizontal asymptote at \( y = 0 \). Adjust the value of \( a \) to fit other possible conditions or points on the graph not explicitly labeled here.
### Equation Input
**y =** [Enter your equation here based on the analysis above.]
This exercise helps in understanding the relationship between equations of rational functions and their graphical representations.
Expert Solution
Step 1
From the given figure, the vertical asymptotes are , horizontal asymptote is and the x intercepts are .
Obtain the equation for the function.
Step by step
Solved in 2 steps
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