# How does the graph of f(x) = log_2(x - 5) - 2 compare to its parent function f(x) = log_2 x?

Sep 7, 2015

${\log}_{2} \left(x - 5\right) - 2$ is ${\log}_{2} \left(x\right)$ shifted down $2$ units, and shifted right $5$ units.

#### Explanation:

For any function $f \left(x\right)$:

$f \left(x\right) + k$ is $f \left(x\right)$ shifted up by $k$ units.

$f \left(x\right) - k$ is $f \left(x\right)$ shifted down by $k$ units.

$f \left(x + k\right)$ is $f \left(x\right)$ shifted left by $k$ units.

$f \left(x - k\right)$ is $f \left(x\right)$ shifted right by $k$ units.

From this we can quickly see that ${\log}_{2} \left(x - 5\right) - 2$ is ${\log}_{2} \left(x\right)$ shifted down $2$ units, and shifted right $5$ units.