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f(x) = 2x² + 8x+1 X+3

f(x) = 2x² + 8x+1 X+3

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

How would you graph the rational function and draw the asymptotes?

The given mathematical function is expressed as: \[ f(x) = \frac{2x^2 + 8x + 1}{x + 3} \] This function is a rational expression where the numerator is a quadratic polynomial \(2x^2 + 8x + 1\), and the denominator is a linear polynomial \(x + 3\). When analyzing this function graphically, key features to consider include possible vertical asymptotes, horizontal asymptotes, and x-intercepts. - **Vertical Asymptote**: This typically occurs where the denominator is zero, which would be at \(x = -3\). - **X-intercepts**: These can be found by setting the numerator equal to zero and solving for \(x\). Detailed analysis of this function would involve polynomial division or factoring to simplify if possible, along with identifying other features such as holes or slant asymptotes depending on the context provided by the function itself.
Transcribed Image Text:The given mathematical function is expressed as: \[ f(x) = \frac{2x^2 + 8x + 1}{x + 3} \] This function is a rational expression where the numerator is a quadratic polynomial \(2x^2 + 8x + 1\), and the denominator is a linear polynomial \(x + 3\). When analyzing this function graphically, key features to consider include possible vertical asymptotes, horizontal asymptotes, and x-intercepts. - **Vertical Asymptote**: This typically occurs where the denominator is zero, which would be at \(x = -3\). - **X-intercepts**: These can be found by setting the numerator equal to zero and solving for \(x\). Detailed analysis of this function would involve polynomial division or factoring to simplify if possible, along with identifying other features such as holes or slant asymptotes depending on the context provided by the function itself.
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