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Transformations of Exponential Functions

Transformations of Exponential Functions 1.7 - Solution

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We want to determine how the graph of the given function compares to the graph of the parent function Notice that in our case so we're looking for transformation(s) of the function Now, let's consider the given function. Looking at the function, we can see that it has been stretched by a factor of translated unit to the right, and translated units up. Let's show these transformations one at a time.

Stretch

Let's start by considering the function If we multiply by we obtain a vertical stretch by a factor of The resulting function is

Horizontal Translation

Now, we need to consider the function This is a horizontal translation of to the right by unit.

Vertical Translation

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