Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question

I just need help finding the expression for this graph please in as much detail as you can muster.

The image displays a graph with the following key features: 1. **Axes**: - The horizontal axis is labeled \(x\). - The vertical axis is labeled \(y\). 2. **Vertical Asymptotes**: - There are two vertical dashed lines (asymptotes) at \(x = -1\) and \(x = 1\). These are indicated by pink dashed lines and labels at the top of each line. 3. **Horizontal Asymptote**: - A horizontal dashed line (asymptote) is present at \(y = 0\), shown as a pink dashed line along the x-axis and labeled horizontally. 4. **Curves**: - There are two main blue curves. - The left curve approaches the vertical asymptote \(x = -1\) from both directions. As \(x\) approaches \(-1\) from the left, the curve moves upwards towards positive infinity. As \(x\) approaches \(-1\) from the right, the curve moves downwards towards negative infinity. - The right curve approaches the vertical asymptote \(x = 1\). As \(x\) approaches \(1\) from the left, the curve rises towards positive infinity. As \(x\) approaches \(1\) from the right, the curve falls towards negative infinity. 5. **Scale**: - Number labels on both axes are indicated at intervals of 3. In summary, the graph likely represents a rational function with vertical asymptotes at \(x = -1\) and \(x = 1\) and a horizontal asymptote at \(y = 0\).
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Transcribed Image Text:The image displays a graph with the following key features: 1. **Axes**: - The horizontal axis is labeled \(x\). - The vertical axis is labeled \(y\). 2. **Vertical Asymptotes**: - There are two vertical dashed lines (asymptotes) at \(x = -1\) and \(x = 1\). These are indicated by pink dashed lines and labels at the top of each line. 3. **Horizontal Asymptote**: - A horizontal dashed line (asymptote) is present at \(y = 0\), shown as a pink dashed line along the x-axis and labeled horizontally. 4. **Curves**: - There are two main blue curves. - The left curve approaches the vertical asymptote \(x = -1\) from both directions. As \(x\) approaches \(-1\) from the left, the curve moves upwards towards positive infinity. As \(x\) approaches \(-1\) from the right, the curve moves downwards towards negative infinity. - The right curve approaches the vertical asymptote \(x = 1\). As \(x\) approaches \(1\) from the left, the curve rises towards positive infinity. As \(x\) approaches \(1\) from the right, the curve falls towards negative infinity. 5. **Scale**: - Number labels on both axes are indicated at intervals of 3. In summary, the graph likely represents a rational function with vertical asymptotes at \(x = -1\) and \(x = 1\) and a horizontal asymptote at \(y = 0\).
Expert Solution
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Step 1: Define the problem

From the given graph 

The horizontal asymptote is y equals 0

The vertical asymptotes are x equals negative 1 spaceand x equals 1

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