Answer: Third Option
[tex]f(x) +3[/tex]
Step-by-step explanation:
The function [tex]y=log_2(x)[/tex] passes through point (2, 1) because the exponential function [tex]2 ^ x = 2[/tex] when [tex]x = 1[/tex].
Then, if the transformed function passes through point (2, 4) then this means that the graph of [tex]y=log_2(x)[/tex] was moved vertically 3 units up.
The transformation that vertically displaces the graph of a function k units upwards is:
[tex]y = f (x) + k[/tex]
Where k is a positive number. In this case [tex]k = 3[/tex]
Then the transformation is:
[tex]f(x) +3[/tex]
and the transformed function is:
[tex]y = log_2 (x) +3[/tex]
