Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 3 - Polynomial and Rational Functions - Section 3.1 Polynomial Functions and Models - 3.1 Assess Your Understanding - Page 208: 60


(a) $x=0,-\sqrt 3,\sqrt 3$ (multiplicity 1). (b) crosses the x-axis at $x=0,\pm\sqrt 3$. (c) $2$. (d) $y=4x^3$.

Work Step by Step

(a) Given $f(x)=4x(x^2-3)=4x(x+\sqrt 3)(x-\sqrt 3)$, we can find zero(s) $x=0,-\sqrt 3,\sqrt 3$ (multiplicity 1). (b) The graph crosses the x-axis at $x=0,\pm\sqrt 3$. (c) The maximum number of turning points on the graph is $n-1=3-1=2$. (d) The end behavior is similar to those of $y=4x^3$.
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