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Identify any horizontal or vertical asymptotes in the graph.

Identify any horizontal or vertical asymptotes in the graph.

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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Identify any horizontal or vertical asymptotes in the graph. 

The image shows the graph of a rational function plotted on a coordinate plane. The plane is divided into a grid, with both x and y axes marked from -10 to 10. ### Graph Description: - **X-Axis:** The horizontal axis (x-axis) is labeled from -10 to 10. - **Y-Axis:** The vertical axis (y-axis) is labeled from -10 to 10. ### Function Characteristics: - **Vertical Asymptote:** There is a vertical asymptote at \( x = 0 \). This is where the graph approaches the line but never touches it. The behavior of the graph near the asymptote shows the function going towards positive infinity as it approaches from the left and negative infinity as it approaches from the right. - **Horizontal Asymptote:** The horizontal asymptote is at \( y = 0 \). The graph approaches this line as the x-values go towards both positive and negative infinity. This indicates that the values of the function get arbitrarily close to zero. ### Graph Behavior: - For \( x < 0 \): The curve exists in the third quadrant, going from negative infinity upwards as it approaches the asymptote at \( x = 0 \). - For \( x > 0 \): The curve is in the first quadrant, descending from positive infinity towards the horizontal asymptote at \( y = 0 \). This graph exemplifies a rational function with both vertical and horizontal asymptotes, displaying typical behavior of such functions.
Transcribed Image Text:The image shows the graph of a rational function plotted on a coordinate plane. The plane is divided into a grid, with both x and y axes marked from -10 to 10. ### Graph Description: - **X-Axis:** The horizontal axis (x-axis) is labeled from -10 to 10. - **Y-Axis:** The vertical axis (y-axis) is labeled from -10 to 10. ### Function Characteristics: - **Vertical Asymptote:** There is a vertical asymptote at \( x = 0 \). This is where the graph approaches the line but never touches it. The behavior of the graph near the asymptote shows the function going towards positive infinity as it approaches from the left and negative infinity as it approaches from the right. - **Horizontal Asymptote:** The horizontal asymptote is at \( y = 0 \). The graph approaches this line as the x-values go towards both positive and negative infinity. This indicates that the values of the function get arbitrarily close to zero. ### Graph Behavior: - For \( x < 0 \): The curve exists in the third quadrant, going from negative infinity upwards as it approaches the asymptote at \( x = 0 \). - For \( x > 0 \): The curve is in the first quadrant, descending from positive infinity towards the horizontal asymptote at \( y = 0 \). This graph exemplifies a rational function with both vertical and horizontal asymptotes, displaying typical behavior of such functions.
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