how to draw the graph of mod x-1?

Dear student,

Please find below the solution to the asked query:

$\mathrm{Note} \mathrm{that} \mathrm{the} \mathrm{mode} \mathrm{function} \mathrm{f}\left(\mathrm{x}\right)=\left|\mathrm{x}\right| \mathrm{is} \mathrm{defined} \mathrm{as},$


$\mathrm{In} \mathrm{a} \mathrm{similar} \mathrm{way}, \mathrm{the} \mathrm{function} \mathrm{f}\left(\mathrm{x}\right)=\left|\mathrm{x}-1\right| \mathrm{can} \mathrm{be} \mathrm{defined} \mathrm{as} \mathrm{follows}:$


$$\begin{gathered} \mathrm{So} \mathrm{the} \mathrm{function} \mathrm{f}\left(\mathrm{x}\right)=\left|\mathrm{x}-1\right| \mathrm{is} \mathrm{a} \mathrm{piecewise} \mathrm{function} \mathrm{taking} \mathrm{seperate} \mathrm{values} \mathrm{on} \mathrm{the} \\ \mathrm{left} \mathrm{and} \mathrm{right} \mathrm{of} \mathrm{the} \mathrm{point} \mathrm{x}=1. \\ \mathrm{To} \mathrm{plot} \mathrm{the} \mathrm{graph} \mathrm{of} \mathrm{this} \mathrm{function}, \mathrm{plot} \mathrm{the} \mathrm{graph} \mathrm{of} \mathrm{the} \mathrm{equations}, \\ \mathrm{y}=-\mathrm{x}+1 \mathrm{for} \mathrm{x}<1 \\ \mathrm{y}=\mathrm{x}-1 \mathrm{for} \mathrm{x}\ge 1 \\ \mathrm{The} \mathrm{graph} \mathrm{of} \mathrm{the} \mathrm{function} \mathrm{will} \mathrm{be} \mathrm{V} \mathrm{shaped} \mathrm{at} \mathrm{x}=1. \\ \mathrm{The} \mathrm{graph} \mathrm{is} \mathrm{shown} \mathrm{below}: \end{gathered}$$



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