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

1 Answer
KillerBunny
Jun 24, 2018

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]}

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