Question

(7.06) what function is represented below

Answer 1

I can eyeball points (1/2, 8), (1,4), (2,1), (3,1/4)

The pattern is each increment of 1/2 in x divides by two.

$f(x) = (\frac k 2)^{2x} = \frac{k}{4^x}$

Any of the points give k=16

$f(x) = 16( 4 ^{-x} ) = 4^{2-x}$

Check: x=1/2 4^(3/2)=2^2=8 good

x=1 4^(2-1)=4 good

x=2 4^(2-2)=1 good

x=3 4^(2-3)=1/4 good