Question

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

Answer 1

Translate the graph of `ln(x)` two units to the right.

Explanation:

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

This kind of transformation, `f(x)\to f(x+k)`, 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(x)` two units to the right: see below the two functions compared.

`y=ln(x)`
graph{ln(x) [-1,10,-10,10]}

`y=ln(x-2)`
graph{ln(x-2) [-1,10,-10,10]}