Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 3 - Test - Page 198: 29

Answer

$\text{Domain: } (-\infty, \infty) \\\text{Range: } (-\infty,-1] $

Work Step by Step

The black graph is the parent graph, $ f(x)=|x| .$ The red graph is the graph of $ f(x)=-|x+2|-1 .$ It is the result of shifting the points of the parent graph $2$ units to the left, reflecting about the $x-$axis, and then shifting $1$ unit down. The $x-$values of the given function, $ g(x)=-|x+2|-1 ,$ can be any real number. The $y-$values are negative real numbers up to $-1$. Hence, the given function has the following characteristics: \begin{array}{l}\require{cancel} \text{Domain: } (-\infty, \infty) \\\text{Range: } (-\infty,-1] .\end{array}
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