A. ![f(x)=3(\frac{1}{2})^x](/tpl/images/0448/6689/4fc27.png)
Step-by-step explanation:
The options are:
![A. f(x)=3(\frac{1}{2})^x\\\\B. f(x)=\frac{1}{2}(3)^x\\\\C. f(x)=(3)^{2x}\\\\ D. f(x)=3^{(\frac{1}{2}x)}](/tpl/images/0448/6689/ab141.png)
For this exercise it is important to remember that, by definition, the Exponential parent functions have the form shown below:
![f(x) = a^x](/tpl/images/0448/6689/613d7.png)
Where "a" is the base.
There are several transformations for a function f(x), some of those transformations are shown below:
1. If
and
, then the function is stretched vertically by a factor of "b".
2. If
and
, then the function is compressed vertically by a factor of "b"
Therefore, based on the information given above, you can identify that the function that represents a vertical stretch of an Exponential function, is the one given in the Option A. This is:
![f(x)=3(\frac{1}{2})^x](/tpl/images/0448/6689/4fc27.png)
Where the factor is:
![b=3](/tpl/images/0448/6689/34d46.png)
And ![31](/tpl/images/0448/6689/c9e7f.png)