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Graph the following rational functions. Be sure to include a chart/table of signs with your graphs and that your graphs include all intercepts and asymptotes. Be sure to show your work in terms of finding the vertical/horizontal asymptotes and the intercepts. y = x²-4 x²-3x

Graph the following rational functions. Be sure to include a chart/table of signs with your graphs and that your graphs include all intercepts and asymptotes. Be sure to show your work in terms of finding the vertical/horizontal asymptotes and the intercepts. y = x²-4 x²-3x

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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**Rational Function Graphing** Graph the following rational function. Be sure to include a chart/table of signs with your graphs and ensure that your graphs include all intercepts and asymptotes. Make sure to show your work in terms of finding the vertical/horizontal asymptotes and the intercepts. **Function:** \[ y = \frac{x^2 - 4}{x^2 - 3x} \] ### Instructions: 1. **Intercepts**: - **X-Intercepts**: Set the numerator equal to zero and solve for \(x\). - **Y-Intercept**: Evaluate the function at \(x = 0\). 2. **Vertical Asymptotes**: - Set the denominator equal to zero and solve for \(x\). 3. **Horizontal Asymptotes**: - Compare the degrees of the numerator and the denominator. 4. **Sign Chart**: - Create a sign chart to determine the signs of the function in different intervals based on the intercepts and asymptotes. Ensure that all calculations, graphs, and analyses are clearly shown and explained.
Transcribed Image Text:**Rational Function Graphing** Graph the following rational function. Be sure to include a chart/table of signs with your graphs and ensure that your graphs include all intercepts and asymptotes. Make sure to show your work in terms of finding the vertical/horizontal asymptotes and the intercepts. **Function:** \[ y = \frac{x^2 - 4}{x^2 - 3x} \] ### Instructions: 1. **Intercepts**: - **X-Intercepts**: Set the numerator equal to zero and solve for \(x\). - **Y-Intercept**: Evaluate the function at \(x = 0\). 2. **Vertical Asymptotes**: - Set the denominator equal to zero and solve for \(x\). 3. **Horizontal Asymptotes**: - Compare the degrees of the numerator and the denominator. 4. **Sign Chart**: - Create a sign chart to determine the signs of the function in different intervals based on the intercepts and asymptotes. Ensure that all calculations, graphs, and analyses are clearly shown and explained.
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