We have
preimage: f(x)=[(1/2)(5^x)]
image: g(x)=-[(1/2)(5^x)] - 3
We know that standard transformations for a function f(x) into g(x) can be done as follows:
g(x)=a*f(x-h)+k
where
a=scale factor for dilation, and a factor of -1 is a reflection about x-axis
h=horizontal shift to the right by h units.
k=vertical shift upwards by k units.
Comparing f(x) and g(x), we can see that
a=-1 (reflection about the x-axis)
h=0 (no horizontal shift)
k=-3 (vertical shift downwards by three units)
So the correct answer is "reflected across the x-axis and 3 units down"
