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 - Chapter Review - Page 228: 23


$g(x)=\left\{ \begin{array}{cc} -2x-7,& \quad \text{if }x\lt -2\\ 2x+1, & \quad \text{if }x \geq -2 \end{array} \right.$

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 $y=g(x)=2|x+2|-3$ $\implies a=2, h=-2$ and $k=-3$ Then, $g(x)$ as a piecewise function is $g(x)=\left\{ \begin{array}{cc} 2[-(x+2)]-3,& \quad \text{if }x+2\lt 0 \\ 2(x+2)-3, & \quad \text{if }x+2 \geq 0 \end{array} \right.$ Simplifying, we get $g(x)=\left\{ \begin{array}{cc} -2x-7,& \quad \text{if }x\lt -2\\ 2x+1, & \quad \text{if }x \geq -2 \end{array} \right.$
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