Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 2 - Functions and Their Graphs - 2.2 The Graph of a Function - 2.2 Assess Your Understanding - Page 69: 52



Work Step by Step

Plugging in $(x-2)$ to $x$ in $f(x)$ to obtain: \begin{align*} f(x-2)&=-(x-2)^2+(x-2)-3\\ &=-(x^2-4x+4)+x-2-3\\ &=-x^2+4x-4+x-5\\ &=-x^2+5x-9 \end{align*}
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