Watch help videoThe function f(x) is defined below. What is the end behavior of f(x)?f(x) = - r3 – 1089x²as x 00, y -0o -0, y →-o∞ and as xas x o0, y -o and as x →-00, y → 00∞,Yas x 00, y 0 and as x→-o0, y → -0∞∞ and as x∞,y →as x 00, y o and as x -o0, y → 0∞∞, YSubmit Answer

Given that : The equation of the polynomial is f(x) = 9 x 2 - x3 - 108.

Answered: as x 00, y -o and as x - 0,y → O

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.6: Quadratic Functions

Problem 58E

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The function f(x) is defined below. What is the end behavior of f(x)?
f(x) = - r3 – 108
9x²
as x 00, y -0o -0, y →-o
∞ and as x
as x o0, y -o and as x →-00, y → 00
∞,Y
as x 00, y 0 and as x→-o0, y → -0∞
∞ and as x
∞,y →
as x 00, y o and as x -o0, y → 0∞
∞, Y
Submit Answer

Expert Solution

Step 1

Given that :

The equation of the polynomial is f(x) = 9 x² - x³ - 108.

Step 2

By using,

End behavior is determine by the degree of the polynomial and the leading coefficient(LC).

For even degree and positive LC :

As x $\to - \infty, f (x) \to \infty . A s x \to \infty, f (x) \to \infty$

For even and negative LC :

As x $\to - \infty, f (x) \to - \infty . A s x \to \infty, f (x) \to - \infty$

For odd degree and positive LC :

As x $\to - \infty, f (x) \to - \infty . A s x \to \infty, f (x) \to \infty$

For odd degree and negative LC :

As x $\to - \infty, f (x) \to \infty . A s x \to \infty, f (x) \to - \infty$

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