# How do you graph  ln(x-2)?

Jun 24, 2018

Translate the graph of $\ln \left(x\right)$ two units to the right.

#### Explanation:

Starting from the parent function $f \left(x\right) = \ln \left(x\right)$, you can see that you're simply computing $f \left(x - 2\right)$.

This kind of transformation, $f \left(x\right) \setminus \to f \left(x + k\right)$, affects the graph by translating it horizontally, $k$ units to the left if $k > 0$, to the right if $k < 0$.

Since in this case $k = - 2$, you simply have to translate the graph of $y = \ln \left(x\right)$ two units to the right: see below the two functions compared.

$y = \ln \left(x\right)$
graph{ln(x) [-1,10,-10,10]}

$y = \ln \left(x - 2\right)$
graph{ln(x-2) [-1,10,-10,10]}