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Can the graph of a polynomial have vertical or horizontal

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 3E Chapter 4.3

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 3E

Can the graph of a polynomial have vertical or horizontal asymptotes? Explain.

Step-by-Step Solution:
Step 1 of 3

Solution: Step1 A polynomial has only nonnegative integer exponents, and have a domain of all real numbers... therefore, there are no vertical asymptotes and no horizontal asymptotes. Step2 F(x)= x^3-9x^2+15x+30 The definition of a vertical asymptote is that it's a discontinuity where F(x) grows without limit as x moves toward a finite value (e.g. when x=2). With a straight polynomial such as F(x)= x^3-9x^2+15x+30 there's no such value; whatever the ups and downs, it's a continuous function over the whole range of x.

Step 2 of 3

Chapter 4.3, Problem 3E is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Can the graph of a polynomial have vertical or horizontal