1. (S8.Purple) Consider the following rational function (x² – x)(x+6) (x – 1)(x+7)(x– 8) r(x) (a) Find the domain of r(x). (b) Find the discontinuities of r(x) and label each as a hole or a vertical asymptote. Explain how you decide if a point is a hole or a vertical asymptote. (c) What terms in r(x) determine the end-behavior? Describe the end-behavior of r(x) using limits. (d) Find the x and y-intercepts of r(x).
1. (S8.Purple) Consider the following rational function (x² – x)(x+6) (x – 1)(x+7)(x– 8) r(x) (a) Find the domain of r(x). (b) Find the discontinuities of r(x) and label each as a hole or a vertical asymptote. Explain how you decide if a point is a hole or a vertical asymptote. (c) What terms in r(x) determine the end-behavior? Describe the end-behavior of r(x) using limits. (d) Find the x and y-intercepts of r(x).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. Consider the following rational function
\[ r(x) = \frac{(x^2 - x)(x + 6)}{(x - 1)(x + 7)(x - 8)} \]
(a) Find the domain of \( r(x) \).
(b) Find the discontinuities of \( r(x) \) and label each as a hole or a vertical asymptote. Explain how you decide if a point is a hole or a vertical asymptote.
(c) What terms in \( r(x) \) determine the end-behavior? Describe the end-behavior of \( r(x) \) using limits.
(d) Find the \( x \)- and \( y \)-intercepts of \( r(x) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4f6f55f-74e4-4811-89c3-6145bf7c8bd8%2F6560ceb2-959c-41a4-bc3c-38ae79033cb5%2Fqvxeoe_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider the following rational function
\[ r(x) = \frac{(x^2 - x)(x + 6)}{(x - 1)(x + 7)(x - 8)} \]
(a) Find the domain of \( r(x) \).
(b) Find the discontinuities of \( r(x) \) and label each as a hole or a vertical asymptote. Explain how you decide if a point is a hole or a vertical asymptote.
(c) What terms in \( r(x) \) determine the end-behavior? Describe the end-behavior of \( r(x) \) using limits.
(d) Find the \( x \)- and \( y \)-intercepts of \( r(x) \).
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