Logarithmic Transformations

Question

State the transformations, in proper order, that are needed to turn f(x)=4log₃(x-2) into g(x)=-2log₃(x+1)

Answer 1

Given f(x) = 4log₃(x-2) and g(x) = -2log₃(x+1) then g(x) = -1/2[f(x+3)]

 

1.  First off we are changing f(x) to f(x+3) when we change (x-2) to (x+1). 

     This will translate 3 units to the left

 

2.  Then we compress the graph by multiplying by a fraction of 1/2

 

3.  Then we reflect the graph about the x-axis by multiplying by -1

 

Note:  You could say that we compress the graph and reflect it about

the x-axis by multiplying by -1/2

 

It doesn't really matter which order you take the transformations in.