Describe the possible end behavior of a polynomial.
Step 1 of 3
Solution: Step1 The end behavior of a polynomial function is the behavior of the graph of f(x)f(x) as xx approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph. The leading coefficient is significant compared to the other coefficients in the function for the very large or very small numbers. So, the sign of the leading coefficient is sufficient to predict the end behavior of the function. Step2 Example Find the end behavior of the function x44x3+3x+25x44x3+3x+25. The degree of the function is even and the leading coefficient is positive. So, the end behavior is: f(x)+, as xf(x)+, as x+f(x)+, as xf(x)+, as x+ The graph looks as follows:
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The answer to “Describe the possible end behavior of a polynomial.” is broken down into a number of easy to follow steps, and 8 words. The full step-by-step solution to problem: 6E from chapter: 4.3 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 6E from 4.3 chapter was answered, more than 382 students have viewed the full step-by-step answer. This full solution covers the following key subjects: behavior, describe, end, polynomial. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.