x - 3 Consider the rational function f(x) x? + 3x + 15 a. What monomial expression best estimates the behavior of x – 3 as x → t oo? Preview b. What monomial expression best estimates the behavior of x + 3x + 15 as x → + oo? Preview c. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates the x – 3 behavior of as x → + o. Simplify your answer as much as possible. x2 + 3x + 15 Preview d. Based on your answer to part (c), what happens to the value of f(x) as x → oo? (Hint: now your answer should be a number, oo, - xx, or "DNE".) As a → ± ∞, f(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
x - 3 Consider the rational function f(x) x? + 3x + 15 a. What monomial expression best estimates the behavior of x – 3 as x → t oo? Preview b. What monomial expression best estimates the behavior of x + 3x + 15 as x → + oo? Preview c. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates the x – 3 behavior of as x → + o. Simplify your answer as much as possible. x2 + 3x + 15 Preview d. Based on your answer to part (c), what happens to the value of f(x) as x → oo? (Hint: now your answer should be a number, oo, - xx, or "DNE".) As a → ± ∞, f(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
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
Related questions
Question
Transcribed Image Text:- 3
Consider the rational function f(x) =
x2 + 3x + 15
a. What monomial expression best estimates the behavior of x – 3 as x → ±o?
Preview
b. What monomial expression best estimates the behavior of x + 3x + 15 as x → ± 0?
Preview
c. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates the
3
behavior of
as x → ± o. Simplify your answer as much as possible.
x2 + 3x + 15
Preview
d. Based on your answer to part (c), what happens to the value of f(x) as x → ± o? (Hint: now your answer
should be a number, ∞,
- 00, or "DNE".)
As x → ± ∞, f(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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