Step 1 :The base function here is \(f(x) = 10^x\). The given function has several transformations applied to it.
Step 2 :\(f(x) = 10^{x+7}\): This is a horizontal shift of 7 units to the left.
Step 3 :\(f(x) = -10^{x+7}\): This is a reflection in the x-axis.
Step 4 :\(f(x) = -\frac{1}{5}10^{x+7}\): This is a vertical compression by a factor of 1/5.
Step 5 :\(f(x) = -\frac{1}{5}10^{x+7} + 12\): This is a vertical shift of 12 units up.
Step 6 :\(\boxed{\text{The transformations applied to the base function are: a horizontal shift of 7 units to the left, a reflection in the x-axis, a vertical compression by a factor of 1/5, and a vertical shift of 12 units up.}}\)