College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 3, Polynomial and Rational Functions - Section 3.2 - Polynomial Functions and Their Graphs - 3.2 Exercises - Page 302: 14

Answer

a. The polynomial function's graph rises to the left end and falls to the right end. b. Graph $IV$

Work Step by Step

End-Behaviour of a Polynomial - Polynomial function of odd degree and positive leading coefficient falls to the left end and rises to the right end. - Polynomial function of odd degree and negative leading coefficient rises to the left end and falls to the right end. - Polynomial function of even degree and positive leading coefficient rises to the left end and right end. - Polynomial function of even degree and negative leading coefficient falls to the left end and right end. a. In this case, $U(x)=-x^3+2x^2$, the function is of odd degree and negative leading coefficient. therefore, the polynomial function's graph rises to the left end and falls to the right end. - Using Descartes rules of signs, we can find that the polynomial has $1$ positive zero and $0$ negative zero and has $0$ as a second zero, therefore the polynomial crosses positive $x$ axis 1 time and doesn't cross negative $x$ axis. b. The graph that matches the description is Graph $IV$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.