Given the equation of the function f(x):
[tex]f(x)=-4\cdot2^{(1-x)}[/tex]
We will use the following rules of the exponents:
[tex]\begin{gathered} a^{m+n}=a^m\cdot a^n \\ a^{-m}=\frac{1}{a^m} \\ a^{mn}=(a^m)^n \end{gathered}[/tex]
So, we can rewrite f(x) as follows:
[tex]\begin{gathered} f(x)=-4\cdot2^{(1-x)} \\ f(x)=-4\cdot2^1\cdot2^{-x} \\ f(x)=-4\cdot2\cdot(2^{-1})^x \\ \\ f(x)=-8\cdot(\frac{1}{2})^x \end{gathered}[/tex]
So, the answer will be option B
