Question

Exponential function

Answer 1

F(x) = -4 * 2^(1-x)
f(x) = -4 * 2^1 / 2^x
f(x) = -8 / 2^x
f(x) = -8 (1/ 2)^x

answer is B. 
f(x) = -8 (1/ 2)^x

Answer 2

We can break the term $2^{1-x}$ apart using the following law of exponents:

$a^{x+y}=a^xa^y$

Applying that, we find that

$2^{1-x}=2^{1+(-x)}=2^1\cdot2^{-x}=2\cdot \frac{1}{2^x}$

Substituting that into our original function, we have

$f(x)=-4\cdot2^{1-x}\\ f(x)=-4\cdot2\cdot \frac{1}{2^x}$

Which we can rewrite in the form $f(x)=ab^x$ as

$f(x)=-8\cdot\big( \frac{1}{2}\big)^x$