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-=-2 61 41 21 -21 41 -61 do 4 X

-=-2 61 41 21 -21 41 -61 do 4 X

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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Question
find the vertical asymptote
### Graph of a Rational Function This diagram depicts the graph of a rational function, showcasing key aspects such as asymptotes and behavior in different quadrants. #### Graph Details: - **Axes**: The graph is plotted on a Cartesian coordinate plane with the x-axis horizontally and the y-axis vertically. - **Asymptotes**: The graph features two asymptotes: - **Vertical Asymptote**: x = 2 (indicated by a dashed vertical red line). - **Horizontal Asymptote**: y = 0 (indicated by a dashed horizontal red line). - **Function Behavior**: - In the first quadrant (I), the function approaches the vertical asymptote x = 2 from the right and the horizontal asymptote y = 0 from above. - In the second quadrant (II), the function approaches the vertical asymptote x = 2 from below and zero as the x-values go to negative infinity. ### Quadrants: The graph is divided into four quadrants: 1. **I (First Quadrant)**: Top right, where x and y are both positive. 2. **II (Second Quadrant)**: Top left, where x is negative and y is positive. 3. **III (Third Quadrant)**: Bottom left, where x and y are both negative. 4. **IV (Fourth Quadrant)**: Bottom right, where x is positive and y is negative. ### Line and Arrow Indicators: - **Arrows on the Axes**: Indicate the direction in which the axes extend (positive and negative directions). - **Red Arrows on the Function**: Show the direction of the graph as it approaches the asymptotes and infinity. ### Conclusion: This graph illustrates the typical behavior of rational functions with vertical and horizontal asymptotes, and its properties in different quadrants.
Transcribed Image Text:### Graph of a Rational Function This diagram depicts the graph of a rational function, showcasing key aspects such as asymptotes and behavior in different quadrants. #### Graph Details: - **Axes**: The graph is plotted on a Cartesian coordinate plane with the x-axis horizontally and the y-axis vertically. - **Asymptotes**: The graph features two asymptotes: - **Vertical Asymptote**: x = 2 (indicated by a dashed vertical red line). - **Horizontal Asymptote**: y = 0 (indicated by a dashed horizontal red line). - **Function Behavior**: - In the first quadrant (I), the function approaches the vertical asymptote x = 2 from the right and the horizontal asymptote y = 0 from above. - In the second quadrant (II), the function approaches the vertical asymptote x = 2 from below and zero as the x-values go to negative infinity. ### Quadrants: The graph is divided into four quadrants: 1. **I (First Quadrant)**: Top right, where x and y are both positive. 2. **II (Second Quadrant)**: Top left, where x is negative and y is positive. 3. **III (Third Quadrant)**: Bottom left, where x and y are both negative. 4. **IV (Fourth Quadrant)**: Bottom right, where x is positive and y is negative. ### Line and Arrow Indicators: - **Arrows on the Axes**: Indicate the direction in which the axes extend (positive and negative directions). - **Red Arrows on the Function**: Show the direction of the graph as it approaches the asymptotes and infinity. ### Conclusion: This graph illustrates the typical behavior of rational functions with vertical and horizontal asymptotes, and its properties in different quadrants.
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