Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 8 - Section 8.5 - Shifting and Reflecting Graphs of Function - Exercise Set - Page 615: 39

Answer

Domain: $(-∞, ∞)$ Range: $(-∞, 3]$

Work Step by Step

Function: $f(x)= -abs(x+2)+3$ There are no fractions in this function, so all real numbers are the domain. The vertex of the graph is at $(-2,3)$. $f(x)= -abs(x+2)+3$ $f(-2)= -abs(-2+2)+3$ $f(-2)= -abs 0 +3$ $f(-2)= -0 +3$ $f(-2) =3$ Since this is the vertex, we know that all possible $y$ values of the function are either greater than or less than $3$. Since the graph opens down, we know that the vertex is the maximum value for $y$.
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