Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 3 - Polynomial and Rational Functions - 3.1 Quadratic Functions and Models - 3.1 Execises - Page 314: 34

Answer

See graph: (a) $(4,2)$. (b) $x=4$. (c) $(-\infty,\infty)$. (d) $(-\infty,2]$. (e) $(-\infty,4)$. ( f ) $(4,\infty)$.

Work Step by Step

See graph: (a) Given $f(x)=-3x^2+24x-46=-3(x^2-8x+16)+2=-3(x-4)^2+2$, we can find its vertex at $(4,2)$. (b) The axis can be found as $x=4$. (c) The domain can be found as $(-\infty,\infty)$. (d) The range can be found as $(-\infty,2]$. (e) the largest open interval of the domain over which the function is increasing can be identified as $(-\infty,4)$. ( f ) the largest open interval over which the function is decreasing can be identified as $(4,\infty)$.
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