Answer :
Answer:
A. [tex]f(x)=3(\frac{1}{2})^x[/tex]
Step-by-step explanation:
The options are:
[tex]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)}[/tex]
For this exercise it is important to remember that, by definition, the Exponential parent functions have the form shown below:
[tex]f(x) = a^x[/tex]
Where "a" is the base.
There are several transformations for a function f(x), some of those transformations are shown below:
1. If [tex]bf(x)[/tex] and [tex]b>1[/tex], then the function is stretched vertically by a factor of "b".
2. If [tex]bf(x)[/tex] and [tex]0<b<1[/tex], 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:
[tex]f(x)=3(\frac{1}{2})^x[/tex]
Where the factor is:
[tex]b=3[/tex]
And [tex]3>1[/tex]