Question

How do i choose a function whose graph will pass through the points?

Answer 1

y = 3^(x-1) fits these data,
y= 3^0 = 1 when x=1
y=3^1 when x=2
y = 3^2 = 9 when x=3 etc.

Log y = (x-1) log 3 would plot as a line on a log-log scale, with slope of log 3.