College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Section 3.5 - Graphing Techniques: Transformations - 3.5 Assess Your Underdstanding: 9


(H) $y=-|x+2|$

Work Step by Step

RECALL: The function $y=a \cdot f(x-h) + k$ involves the following transformations of the parent function $f(x)$: The graph looks like an inverted V, so its parent function is $y=|x|$. The graph of the parent function is shaped like an upward V. The given graph is an downward V, so it must involve a reflection about the x-axis of the parent function. Thus, a tentative equation of the function is $y=-|x|$ The vertex of the given function is a $(-2, 0)$. This means that the graph involves a horizontal shift of $2$ units to the left of the parent function $f(x)$. Thus, the tentative equation becomes $y=-|x+2|$. Therefore, the equation of the given graph is $y=-|x+2|$.
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