Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 4 - Writing Linear Functions - 4.7 - Piecewise Functions - Exercises - Page 223: 45

Answer

$g(x)=\left\{ \begin{array}{cc} x-1,& \quad \text{if }x\lt 3\\ -x+5, & \quad \text{if }x \geq 3 \end{array} \right.$

Work Step by Step

The absolute value function $g(x)=a|x-h|+k$ can be written as a piecewise function. $g(x)=\left\{ \begin{array}{cc} a[-(x-h)]+k,& \quad \text{if }x-h\lt 0 \\ a(x-h)+k, & \quad \text{if }x-h \geq 0 \end{array} \right.$ Given $y=g(x)=-|x-3|+2$ $\implies a=-1, h=3$ and $k=2$ Then, $g(x)$ as a piecewise function is $g(x)=\left\{ \begin{array}{cc} -1[-(x-3)]+2,& \quad \text{if }x-3\lt 0 \\ -1(x-3)+2, & \quad \text{if }x-3 \geq 0 \end{array} \right.$ Simplifying, we get $g(x)=\left\{ \begin{array}{cc} x-1,& \quad \text{if }x\lt 3\\ -x+5, & \quad \text{if }x \geq 3 \end{array} \right.$
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