## Calculus: Early Transcendentals (2nd Edition)

$s\,\left( x \right) = \left\{ \begin{gathered} 1\,\,\,\,\,\,\,\,if\,\,\,\,\,\,\,\,\,x > 0 \hfill \\ \hfill \\ - 1\,\,\,\,\,\,\,if\,\,\,\,\,\,\,x < 0 \hfill \\ \end{gathered} \right.$
$\begin{gathered} Function\,\,f\,\left( x \right) = \left| x \right|\,\,can\,be\,\,\,\,written\,\, \hfill \\ {\text{using the definiton of absolute value}} \hfill \\ \hfill \\ f\,\left( x \right) = \left\{ \begin{gathered} x\,\,\,\,\,\,\,\,if\,\,\,\,\,\,\,\,x <0 \hfill \\ \hfill \\ - x\,\,\,\,\,if\,\,\,\,\,\,\,\,x < 0 \hfill \\ \end{gathered} \right. \hfill \\ \hfill \\ since\,\,the\,slope\,of\,\,the\,line\,f\,\left( x \right) = x\,is\,1\,\,and\,slope \hfill \\ of\,the\,line\,f\,\left( x \right) = - x\,\,is\,\, - 1\,,\,slope\,function\,is\,given\,\,by \hfill \\ \hfill \\ s\,\left( x \right) = \left\{ \begin{gathered} 1\,\,\,\,\,\,\,\,if\,\,\,\,\,\,\,\,\,x > 0 \hfill \\ \hfill \\ - 1\,\,\,\,\,\,\,if\,\,\,\,\,\,\,x < 0 \hfill \\ \end{gathered} \right. \hfill \\ \hfill \\ \end{gathered}$