Question

a. Complete the table.
х
f(x) = 2(2)*
=
-2 -1
0
1
2
1

Answer 1

Answer:

1/2,1,2,4,8 in order

Step-by-step explanation:

Given:

$\displaystyle \large{f(x)=2(2)^x}$

The function can be simplified to:

$\displaystyle \large{f(x)=2^{x+1}}$ via law of exponent.

Recall:

$\displaystyle \large{a^m\cdot a^n=a^{m+n}}$

Next, substitute given x-values in:

$\displaystyle \large{f(-2)=2^{-2+1}=2^{-1}=\dfrac{1}{2}}\\\displaystyle \large{f(-1)=2^{-1+1}=2^0=1}\\\displaystyle \large{f(0)=2^{0+1}=2^1=2}\\\displaystyle \large{f(1)=2^{1+1}=2^2=4}\\\displaystyle \lage{f(2)=2^{2+1}=2^3=8}$

Therefore, the solution is 1/2,1,2,4,8