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6. Write a rational function which has the following information: Vertical asymptotes are x=5 and x= -1 Horizontal asymptote is y=0 Removable discontinuity (holes) at x=2 Then graph your function.

6. Write a rational function which has the following information: Vertical asymptotes are x=5 and x= -1 Horizontal asymptote is y=0 Removable discontinuity (holes) at x=2 Then graph your function.

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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**Rational Function Problem:** **Task:** Write a rational function that has the following properties: - **Vertical Asymptotes:** \(x = 5\) and \(x = -1\) - **Horizontal Asymptote:** \(y = 0\) - **Removable Discontinuity (hole):** at \(x = 2\) **Graphing Task:** Then graph your function. **Graph Description:** The graph is represented by a pair of perpendicular axes, standard in Cartesian coordinates, with arrows indicating the positive and negative directions for both the x-axis and y-axis. - The horizontal axis is the x-axis. - The vertical axis is the y-axis. You'll need to plot the function based on the derived rational equation according to the given conditions. The critical points to pay attention to are the vertical asymptotes at \(x = 5\) and \(x = -1\), and the removable discontinuity at \(x = 2\). The horizontal asymptote indicates that the graph approaches the x-axis but never touches or crosses it.
Transcribed Image Text:**Rational Function Problem:** **Task:** Write a rational function that has the following properties: - **Vertical Asymptotes:** \(x = 5\) and \(x = -1\) - **Horizontal Asymptote:** \(y = 0\) - **Removable Discontinuity (hole):** at \(x = 2\) **Graphing Task:** Then graph your function. **Graph Description:** The graph is represented by a pair of perpendicular axes, standard in Cartesian coordinates, with arrows indicating the positive and negative directions for both the x-axis and y-axis. - The horizontal axis is the x-axis. - The vertical axis is the y-axis. You'll need to plot the function based on the derived rational equation according to the given conditions. The critical points to pay attention to are the vertical asymptotes at \(x = 5\) and \(x = -1\), and the removable discontinuity at \(x = 2\). The horizontal asymptote indicates that the graph approaches the x-axis but never touches or crosses it.
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