Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.5 - Transformations of Functions - 2.5 Exercises - Page 211: 32


a) $f(x)=[[x]]$ b) Reflection across the $x$-axis, vertical shift c) See graph d) $g(x)=-f(x)+1$

Work Step by Step

We are given the function: $g(x)=-[[x]]+1$ a) The parent function is: $f(x)=[[x]]$ b) Reflect $f(x)$ across the $x$-axis to get $a(x)=-[[x]]$. Vertically shift $a(x)$ one unit upward to get $g(x)=-[[x]]+1$. c) Graph the function $g$. d) Use function notation to write $g$ in terms of $f$: $g(x)=-f(x)+1$
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