Modulus functions of the form [math]y=|f\left(x\right)|[/math]

For[math]y=\left|f\left(x\right)\right|,[/math] the graph of [math]y=f\left(x\right)[/math] that is above x-axis ([math]y\ge0[/math]) is preserved; the graph that is below the x-axis ([math]y<0[/math]) is reflected about the x-axis.

Modulus function of the form [math]y=f\left(\left|x\right|\right)[/math].

For [math]y=f\left(\left|x\right|\right),[/math]the graph of [math]y=f\left(x\right)[/math] when [math]x\ge0[/math] is reflected along the y-axis to replace the graph of [math]y=f\left(x\right)[/math] when [math]x<0[/math].