Question

What would translate the function f(x) = log(2)x two units down and three units to the right?
The base is two

Answer 1

\[f \left( x \right)= \log _{2}\left( x-3 \right)-2\]

Answer 2

Plug in \[\left( x-h \right)\] for \[x\] to shift h units to the right (if h > 0, to the left if h < 0).
If \[k>0\] then \[f \left( x \right)+k\] will shift \[f \left( x \right)\]up k units and if you change the + to a - then it shifts it down k units.