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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We want to graph the given function $g(x)=e_{-5x}+2$ as a transformation of the function $f(x)=e_{-x}.$ $g(x)=e_{-5x}+2 $ Looking at the function, we can see that it has been horizontally shrinked by a factor of $5$ and translated $2$ units up. Let's show the transformations one at a time.

If we multiply the $x-$variable in $f(x)=e_{-x}$ by $5,$ we obtain a horizontal shrink by a factor of $5.$ The resulting function is $y=e_{-5x}.$

Finally, we will consider the function $g(x)=e_{-5x}+2.$ This is a vertical translation of $y=e_{-5x}$ up by $2$ units.