Transformations of Exponential Functions

We want to graph the given function $k(x)=2^{x-2}+2$ as a transformation of the function $y=2^x.$ $$\begin{array}{c}k(x)=2^{x-2}+2\end{array}$$ Looking at the function, we can see that it has been translated $2$ units to the right and $2$ units up. Let's show the transformations one at a time.

Horizontal Translation

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

Vertical Translation

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

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