Match the graph of the function with the function rule

As seen from the graph, the y intercept is (0,0.5)

plugging this value in each equation:

y=1*4^x

plugging x as 0 and y as 0.5

lhs≠rhs

plugging x as 0 and y as 0.5

lhs≠rhs

plugging x as 0 and y as 0.5

lhs = rhs

so answer is

the first one, all those points on the line just make a strait line.

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents