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: 30

Answer

See graph: (a) $(-3,-4)$. (b) $x=-3$. (c) $(-\infty,\infty)$. (d) $[-4,\infty)$. (e) $(-3,\infty)$. ( f ) $(-\infty,-3)$.

Work Step by Step

See graph: (a) Given $f(x)=x^2+6x+5=(x+3)^2-4$, we can find its vertex at $(-3,-4)$. (b) The axis can be found as $x=-3$. (c) The domain can be found as $(-\infty,\infty)$. (d) The range can be found as $[-4,\infty)$. (e) the largest open interval of the domain over which the function is increasing can be identified as $(-3,\infty)$. ( f ) the largest open interval over which the function is decreasing can be identified as $(-\infty,-3)$.
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