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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We want to graph the given function $g(x)=-2_{x−3}$ as a transformation of the function $f(x)=2_{x}.$ $g(x)=-2_{x−3} $ Looking at the function, we can see that it has been reflected in the $x-$axis and translated $3$ units to the right. Let's show the transformations one at a time.

Let's start by considering the parent function $f(x)=2_{x}.$ If we perform a reflection across the $x-$axis, the resulting function is $y=-2_{x}.$

Now, we need to consider the function $g(x)=-2_{x−3}.$ This is a horizontal translation of $y=-2_{x}$ to the right by $3$ units.