A b c х — 6Consider the rational function f(x)x2 + 3x + 18a. What monomial expression best estimates the behavior of x – 6 as x → ±∞?Previewb. What monomial expression best estimates the behavior of x? + 3x + 18 as x → ± 0?Previewc. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates theх — 6behavior ofx2 + 3xas x → + 0. Simplify your answer as much as possible.18Previewd. Based on your answer to part (c), what happens to the value of f(x) as x → ±∞? (Hint: now your answershould be a number, ∞,o, or "DNE".)As x → ±», ƒ(x) →Previewe. Based on your answer to part (d), what is the horizontal asymptote of f? If no horizontal asymptote exists forf, enter "DNE".y =Preview

Solution ) f(x) = (x - 6 )/(x2 + 3x + 18) a) monomial expression that best estimate the behaviour of…

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

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.2: Polynomial Functinos And Their Graphs

Problem 2E: Describe the end behavior of each polynomial. (a) y=x38x2+2x15 End behavior: y as x y as x (b)...

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Question

A b c

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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