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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We want to graph the given function $f(x)=2_{x+2}−2$ as a transformation of the function $y=2_{x}.$ $f(x)=2_{x+2}−2⇔f(x)=2_{x−(-2)}+(-2) $ Looking at the equation, we can see that the function has been translated $2$ units to the left and $2$ units down. Let's show the transformations one at a time.

Firstly, let's consider the function $y=2_{x+2}.$ This is a horizontal translation of $y=2_{x}$ to the left by $2$ units.

Finally, we will consider the function $f(x)=2_{x+2}−2.$ This is a vertical translation of $y=2_{x+2}$ down by $2$ units.

Therefore, we can notice that the obtained graph is shown in choice **C**.