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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We want to determine how the graph of the given function compares to the graph of the parent function $y=b_{x}.$ Notice that in our case $b=2,$ so we're looking for transformation(s) of the function $y=2_{x}.$ Now, let's consider the given function. $y=3(2)_{x−1}+4 $ Looking at the function, we can see that it has been stretched by a factor of $3,$ translated $1$ unit to the right, and translated $4$ units up. Let's show these transformations one at a time.

Let's start by considering the function $y=2_{x}.$ If we multiply $2_{x}$ by $3,$ we obtain a vertical stretch by a factor of $3.$ The resulting function is $y=3(2)_{x}.$

Now, we need to consider the function $y=3(2)_{x−1}.$ This is a horizontal translation of $y=3(2)_{x}$ to the right by $1$ unit.

Finally, we will consider the function $y=3(2)_{x−1}+4.$ This is a vertical translation of $y=3(2)_{x−1}$ up by $4$ units.