By the "end behavior" of a function we mean the behavior of its values as →∞ and a to - ∞o. Do P(x) = 4x5 - 5x³ + 2x andQ(x) = 4x5 have the same end behavior? Answer "y" for yes or "n" for no below.

Answered: By the "end behavior" of a function we…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Question

By the "end behavior" of a function we mean the behavior of its values as →∞ and a to - ∞o. Do P(x) = 4x5 - 5x³ + 2x and
Q(x) = 4x5 have the same end behavior? Answer "y" for yes or "n" for no below.

Expert Solution

Step 1

P(x)=4x⁵-5x³+2x

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

The degree of this polynomial is the greatest exponent, or 5 .The leading coefficient is the coefficient of the term with the greatest exponent, or

+4.For polynomials of even degree, the "ends" of the polynomial graph point in the same direction as follows.

Even degree and positive LC:

As x→−∞ , f(x)→∞ As x→∞ , f(x)→∞Even degree and negative LC:As x→−∞ , f(x)→−∞ As x→∞, f(x)→−∞ For polynomials of odd degree, the "ends" of the polynomial graph point in opposite directions as follows (note, there is a saying that Odd means Opposite when graphing).Odd degree and positive LC: