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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We want to graph the given function $g(x)=(31 )_{x+2}−32 $ as a transformation of the function $f(x)=(31 )_{x}.$ $g(x)=(31 )_{x+2}−32 ⇔g(x)=(31 )_{x−(-2)}+(-32 ) $ Looking at the function, we can see that it has been translated $2$ units to the left and $32 $ units down. Let's show the transformations one at a time.

Firstly, let's consider the function $y=(31 )_{x+2}.$ This is a horizontal translation of $f(x)=(31 )_{x}$ to the left by $2$ units.

Finally, we will consider the function $g(x)=(31 )_{x+2}−32 .$ This is a vertical translation of $y=(31 )_{x+2}$ down by $32 $ units.