I- 4 Consider the rational function f(x) =137 + 16 %3D a. What monomial expression best estimates the behavior of z - 4 as z + t o0? Preview b. What monomial expression best estimates the behavior of z2 + 3z + 16 as z ± oo? Preview I - 4 c. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates the behavior of as 22 + 3x + 16 I + t 00. Simplify your answer as much as possible. Preview ld he a number

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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Question
x - 4
Consider the rational function f(x)
x2 +3x + 16
a. What monomial expression best estimates the behavior of z - 4 as x ± o?
Preview
b. What monomial expression best estimates the behavior of x2 + 3x + 16 as x → ±o?
Preview
- 4
c. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates the behavior of
as
x2 + 3x + 16
x too. Simplify your answer as much as possible.
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, oo, -∞
or "DNE".)
As x ± 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
Submit
Transcribed Image Text:x - 4 Consider the rational function f(x) x2 +3x + 16 a. What monomial expression best estimates the behavior of z - 4 as x ± o? Preview b. What monomial expression best estimates the behavior of x2 + 3x + 16 as x → ±o? Preview - 4 c. Using your results from parts (a) and (b), write a ratio of monomial expressions that best estimates the behavior of as x2 + 3x + 16 x too. Simplify your answer as much as possible. 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, oo, -∞ or "DNE".) As x ± 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 Submit
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