Function $$g$$ can be thought of as a scaled version of $$f(x)=|x|$$. What is the equation for $$g(x)$$ ? ![](http://admin.getprephub.com/media/editor/pe5_20221125205456559571.png)

The equation of a scaled transformation of the graph of $${f}({x})=|{x}|$$ can have the form: $${g}({x})={a}|x|$$. If $$|a|>1$$, the graph is stretched vertically, and if $$|a|<1$$, the graph is compressed vertically. When $$a<0$$, the graph is then reflected across the $${X}$$-axis. Let us take corresponding points in $${f}$$ and $$g$$.For example, $$f(5)=5$$ and $$g(5)=-1$$. $$\frac{g(5)}{f(5)}=-0.2$$ Each y-coordinate in $${g}$$ is $$0.2$$ times the distance from the $${x}$$-axis as the corresponding y-coordinate in $${f}$$, but on the opposite side of the $${X}$$-axis. So, $${a}=-0.2$$ ![](http://admin.getprephub.com/media/editor/pes5_20221125205516584689.png) So , the new graph is $$g=-0.2|{x}|$$

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MCQ

Function $g$ can be thought of as a scaled version of $f(x)=|x|$ . What is the equation for $g(x)$ ?

Select all that apply :

$g=-0.2|x|$

$g=0.2|{x}|$

${g}=-0.2+|{x}|$

$\quad g=0.2-|{x}|$

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