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Use the graph to write an equation for the function. y = 4 (0, 1) -6 -4 -2 2 4 4 6" 2. 2.

Use the graph to write an equation for the function. y = 4 (0, 1) -6 -4 -2 2 4 4 6" 2. 2.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Use the graph to write an equation for the function.** \[ y = \] **Graph Explanation:** The graph features a hyperbola, which appears typical of functions with rational expressions. Key elements observed include: - **Axes:** The horizontal axis is labeled as \( x \), and the vertical axis is labeled as \( y \). - **Asymptotes:** - A vertical asymptote is present at \( x = -2 \), indicated by a dashed orange line. This suggests the function is undefined at \( x = -2 \). - **Point of Interest:** - The graph passes through the point \( (0, 1) \). This point is likely crucial in determining the specific form of the function. - **Behavior:** - As \( x \) approaches \(-2\) from the left, \( y \) tends towards negative infinity, and from the right, it tends towards positive infinity. - The function decreases towards zero as \( x \) moves towards both positive and negative infinity, indicating horizontal asymptotic behavior along the \( x \)-axis. This graph can likely be represented by a function of the form: \[ y = \frac{a}{x + 2} + b \] Where \( a \) and \( b \) are constants. Given the point \( (0, 1) \), solving for these constants will provide the specific equation.
Transcribed Image Text:**Use the graph to write an equation for the function.** \[ y = \] **Graph Explanation:** The graph features a hyperbola, which appears typical of functions with rational expressions. Key elements observed include: - **Axes:** The horizontal axis is labeled as \( x \), and the vertical axis is labeled as \( y \). - **Asymptotes:** - A vertical asymptote is present at \( x = -2 \), indicated by a dashed orange line. This suggests the function is undefined at \( x = -2 \). - **Point of Interest:** - The graph passes through the point \( (0, 1) \). This point is likely crucial in determining the specific form of the function. - **Behavior:** - As \( x \) approaches \(-2\) from the left, \( y \) tends towards negative infinity, and from the right, it tends towards positive infinity. - The function decreases towards zero as \( x \) moves towards both positive and negative infinity, indicating horizontal asymptotic behavior along the \( x \)-axis. This graph can likely be represented by a function of the form: \[ y = \frac{a}{x + 2} + b \] Where \( a \) and \( b \) are constants. Given the point \( (0, 1) \), solving for these constants will provide the specific equation.
Expert Solution
Step 1

In the above graph at x=0 the function gives the value F=1, 

similarly at x=3, F=0 and at x=-4, F=0

Hence 3 and -4 are roots of the function and Y=-2 is an asymptote to the function F.

So, F= {(3-x)(x+4)}/6(x+2)

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