Question 756419
The basic graph is for y=log(2,x), easily sketched using a few simple points.

{{{graph(250,250,-10,10,-10,10,log(2,x))}}}


The (x-4) part shifts to the right by 4 units.


{{{graph(250,250,-10,10,-10,10,log(2,x-4))}}}


The (2/3) factor squashes the graph vertically by that factor.
{{{graph(250,250,-10,10,-10,10,(2/3)log(2,x-4))}}}


The +1 moves the graph upward by 1 unit.


{{{graph(250,250,-10,10,-10,10,(2/3)log(2,x-4)+1)}}}

Note: The site system is not rendering properly.  The graph should decrease rapidly as it goes toward the left; NOT be cut-off.  There IS an vertical asymptote on the left of the graph.  x=4 is this vertical asymtptote.