It is known that some rational function satisfies all of the following properties: (i) it has a vertical asymptote at x = 2 and no other vertical asymptote (ii) it has an oblique asymptote with equation: y = 3x - 1 as x → +0 , and as x → -00 (iii) the value of its y-intercept is-3 (iv) it has no x intercept. Based on the given information, answer the following questions: a) Is there a unique function, or many functions satisfying all the conditions given?: Justify below how you can know this fact without doing any algebraic work: b) Find the simplest equation possible equation for this function. Answer: The equation I found is: Fully show how your work in determining this answer, and verifying that all given statements apply to your answer.

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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It is known that some rational function satisfies all of the following properties:
(i) it has a vertical asymptote at x = 2 and no other vertical asymptote
(ii) it has an oblique asymptote with equation: y = 3x - 1 as x → +0 , and as x → -00
(iii) the value of its y-intercept is-3
(iv) it has no x intercept.
Based on the given information, answer the following questions:
a) Is there a unique function, or many functions satisfying all the conditions given?:
Justify below how you can know this fact without doing any algebraic work:
b) Find the simplest equation possible equation for this function.
Answer: The equation I found is:
Fully show how your work in determining this answer, and verifying that all given statements
apply to your answer.
Transcribed Image Text:It is known that some rational function satisfies all of the following properties: (i) it has a vertical asymptote at x = 2 and no other vertical asymptote (ii) it has an oblique asymptote with equation: y = 3x - 1 as x → +0 , and as x → -00 (iii) the value of its y-intercept is-3 (iv) it has no x intercept. Based on the given information, answer the following questions: a) Is there a unique function, or many functions satisfying all the conditions given?: Justify below how you can know this fact without doing any algebraic work: b) Find the simplest equation possible equation for this function. Answer: The equation I found is: Fully show how your work in determining this answer, and verifying that all given statements apply to your answer.
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