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х — 6 Consider the rational function f(x) x2 + 3x + 18 a. What monomial expression best estimates the behavior of x - 6 as x → ± oo? Preview b. What monomial expression best estimates the behavior of x2 + 3x + 18 as x + o? Preview c. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates the х — 6 behavior of as x → + o. Simplify your answer as much as possible. x2 + 3x + 18 Preview

х — 6 Consider the rational function f(x) x2 + 3x + 18 a. What monomial expression best estimates the behavior of x - 6 as x → ± oo? Preview b. What monomial expression best estimates the behavior of x2 + 3x + 18 as x + o? Preview c. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates the х — 6 behavior of as x → + o. Simplify your answer as much as possible. x2 + 3x + 18 Preview

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.5: Graphing Rational Functions
Problem 42PS
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х — 6 Consider the rational function f(x) x2 + 3x + 18 a. What monomial expression best estimates the behavior of x – 6 as x → ±∞? Preview b. What monomial expression best estimates the behavior of x? + 3x + 18 as x → ± 0? Preview c. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates the х — 6 behavior of x2 + 3x as x → + 0. Simplify your answer as much as possible. 18 Preview d. Based on your answer to part (c), what happens to the value of f(x) as x → ±∞? (Hint: now your answer should be a number, ∞, o, or "DNE".) As x → ±», ƒ(x) → Preview e. Based on your answer to part (d), what is the horizontal asymptote of f? If no horizontal asymptote exists for f, enter "DNE". y = Preview
Transcribed Image Text:х — 6 Consider the rational function f(x) x2 + 3x + 18 a. What monomial expression best estimates the behavior of x – 6 as x → ±∞? Preview b. What monomial expression best estimates the behavior of x? + 3x + 18 as x → ± 0? Preview c. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates the х — 6 behavior of x2 + 3x as x → + 0. Simplify your answer as much as possible. 18 Preview d. Based on your answer to part (c), what happens to the value of f(x) as x → ±∞? (Hint: now your answer should be a number, ∞, o, or "DNE".) As x → ±», ƒ(x) → Preview e. Based on your answer to part (d), what is the horizontal asymptote of f? If no horizontal asymptote exists for f, enter "DNE". y = Preview
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