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The graph has a vertical asymptote at x = 3, a horizontal asymptote at y = 0, and passes through the point (4, 2). What could be the function of this graph? 10 8 C

The graph has a vertical asymptote at x = 3, a horizontal asymptote at y = 0, and passes through the point (4, 2). What could be the function of this graph? 10 8 C

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem Statement:** The graph has a vertical asymptote at \( x = 3 \), a horizontal asymptote at \( y = 0 \), and passes through the point \( (4, 2) \). What could be the function of this graph? **Graph Explanation:** The graph features a blue curve with the following characteristics: - **Vertical Asymptote** at \( x = 3 \): The curve approached \( x = 3 \) but never crosses this vertical line. - **Horizontal Asymptote** at \( y = 0 \): The curve approaches the x-axis but never touches it as \( x \) approaches infinity. - **Passes through the Point** \( (4, 2) \): The curve includes the point (4, 2) on the graph. **Graph Image Description:** The graph is plotted on a Cartesian plane, with the x-axis ranging from -10 to 10 and the y-axis ranging from -10 to 10. The curve exhibits behavior typically associated with rational functions that have vertical and horizontal asymptotes. **Possible Functions:** 1. \( y = \frac{-4}{x + 4} \) 2. \( y = \frac{4}{x - 3} \) 3. \( y = \frac{-2}{x + 4} \) 4. \( y = \frac{2}{x - 3} \) Select the correct function that matches the given characteristics of the graph.
Transcribed Image Text:**Problem Statement:** The graph has a vertical asymptote at \( x = 3 \), a horizontal asymptote at \( y = 0 \), and passes through the point \( (4, 2) \). What could be the function of this graph? **Graph Explanation:** The graph features a blue curve with the following characteristics: - **Vertical Asymptote** at \( x = 3 \): The curve approached \( x = 3 \) but never crosses this vertical line. - **Horizontal Asymptote** at \( y = 0 \): The curve approaches the x-axis but never touches it as \( x \) approaches infinity. - **Passes through the Point** \( (4, 2) \): The curve includes the point (4, 2) on the graph. **Graph Image Description:** The graph is plotted on a Cartesian plane, with the x-axis ranging from -10 to 10 and the y-axis ranging from -10 to 10. The curve exhibits behavior typically associated with rational functions that have vertical and horizontal asymptotes. **Possible Functions:** 1. \( y = \frac{-4}{x + 4} \) 2. \( y = \frac{4}{x - 3} \) 3. \( y = \frac{-2}{x + 4} \) 4. \( y = \frac{2}{x - 3} \) Select the correct function that matches the given characteristics of the graph.
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