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Transformations of Exponential Functions

We want to graph the given function as a transformation of the function Looking at the equation, we can see that the function has been translated units to the left and units down. Let's show the transformations one at a time.

Horizontal Translation

Firstly, let's consider the function This is a horizontal translation of to the left by units.

Vertical Translation

Finally, we will consider the function This is a vertical translation of down by units.

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