identify the type of variation represented in the table and name the y-value when x=32. x: 2,4,8,16, 32 y: 4, 2, 1, 0.5, ?

Answer 1

every x value is twice the previous
every y value is half the previous
so if x = 32 then y = 0.25

well if n = 1 is your first point and n = 2 is your second etc then
x = 2^n
and
y = 4/2^(n-1) = 2^2 * 2^(1-n) =2^(3-n)
so
x/y = 2^n/2^(3-n) = 2^(2n-3)
y = x * 2^(3-2n)