Which of the following is a transformation applied to the base function of $f(x)=-\frac{1}{5}\left(10^{x+7}\right)+12 ?$
Answer
\(\boxed{\text{The transformations applied to the base function are: a horizontal shift of 7 units to the left, a reflection in the x-axis, a vertical compression by a factor of 1/5, and a vertical shift of 12 units up.}}\)
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 ：\(\boxed{\text{The transformations applied to the base function are: a horizontal shift of 7 units to the left, a reflection in the x-axis, a vertical compression by a factor of 1/5, and a vertical shift of 12 units up.}}\)
