## The Graph of a Function When the Modulus of x is Used

Given the graph of a function,we can sketch the graph ofby considering the effect of taking the modulus ofon positive and negative values of

Forso the part of the graph for whichis unchanged.

ForThis means thatso that the point to be plotted iswhich is just the pointreflected in the– axis. The effect of taking the modulus of each value ofis then to erase the part of the graph left of the- axis and replace it by the reflection in the- axis of the part of the graph to the right of the y axis.

Example: To plotdraw the part of the graph forand reflect this part of the graph in the- axis to obtain the part of the graph forThe union of these two parts is