Question

A. Complete the table.

х
f(x) = 2(2)*
=
-2 -1
0
1
2
1

Answer 1

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

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)=(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