Answer:
B.
Step-by-step explanation:
To find the right exponential function, we can just take x-values an replace them into the given functions. The one that give the correct y-values will be the answer.
For \(x=-2\), let's see which function gives \(y=-\frac{1}{8}\)
\(y=8(4)^{x-1} \\y=8(4)^{-2-1}\\ y=8(4)^{-3}\\ y=\frac{8}{4^{3} }=\frac{1}{8}\)
You can observe that function A is not the correct one, because it gives a positive result. However, function B can actually be the answer, because it woud give the same y-value than A but negative, as we need. Let's see
\(y=-8(4)^{x-1}\\ y=-8(4)^{-2-1}\\ y=-8(4)^{-3}\\ y=-\frac{8}{4^{3} }=-\frac{1}{8}\)
Let's evalute for \(x=0\)
\(y=-8(4)^{0-1}=-8(4)^{-1}= -\frac{8}{4}=-2\)
Which is right.
Therefore, the right answer is B.
