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-4-3-2 VA 3 2 1-2 x = – 1 y = 1 3 4 5 x x = 2

-4-3-2 VA 3 2 1-2 x = – 1 y = 1 3 4 5 x x = 2

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.6: More On Graphing Rational Functions
Problem 28PS
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Question

I need help finding a equation that fits this graph.

The image is a graph depicting the function \( f(x) \) with vertical and horizontal asymptotes, as well as significant points marked on the Cartesian plane. Below is a detailed description: - **Axes:** - The horizontal axis is labeled as the \( x \)-axis. - The vertical axis is labeled as the \( y \)-axis. - **Asymptotes:** - A vertical asymptote is drawn as a dashed pink line at \( x = -1 \). - Another vertical asymptote is drawn as a dashed pink line at \( x = 2 \). - A horizontal asymptote is placed at \( y = 1 \) with a dashed pink line. - **Curve:** - The curve approaches the vertical asymptote at \( x = -1 \) from both sides. - The curve descends towards the asymptote at \( x = 2 \) and moves away on the other side. - There is a smooth transition just below the horizontal asymptote \( y = 1 \) as \( x \) increases. - **Labeled Points:** - Points along the \( x \)-axis are labeled at intervals: \(-4, -3, -2, 1, 3, 4, 5\). - Points along the \( y \)-axis are labeled at values: \(-2, -1, 1, 2, 3\). The overall behavior illustrated is typical of a rational function involving vertical and horizontal asymptotes, showing two branches of the curve that approach the asymptotes yet do not intersect them.
Transcribed Image Text:The image is a graph depicting the function \( f(x) \) with vertical and horizontal asymptotes, as well as significant points marked on the Cartesian plane. Below is a detailed description: - **Axes:** - The horizontal axis is labeled as the \( x \)-axis. - The vertical axis is labeled as the \( y \)-axis. - **Asymptotes:** - A vertical asymptote is drawn as a dashed pink line at \( x = -1 \). - Another vertical asymptote is drawn as a dashed pink line at \( x = 2 \). - A horizontal asymptote is placed at \( y = 1 \) with a dashed pink line. - **Curve:** - The curve approaches the vertical asymptote at \( x = -1 \) from both sides. - The curve descends towards the asymptote at \( x = 2 \) and moves away on the other side. - There is a smooth transition just below the horizontal asymptote \( y = 1 \) as \( x \) increases. - **Labeled Points:** - Points along the \( x \)-axis are labeled at intervals: \(-4, -3, -2, 1, 3, 4, 5\). - Points along the \( y \)-axis are labeled at values: \(-2, -1, 1, 2, 3\). The overall behavior illustrated is typical of a rational function involving vertical and horizontal asymptotes, showing two branches of the curve that approach the asymptotes yet do not intersect them.
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