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Which answer describes the transformation of f(x)=log 2 (x−5)−2 from the parent function g(x)=log 2 x ?

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Which answer describes the transformation of f(x)=log2(x−5)−2 from the parent function g(x)=log2 x ?

It is the graph of g(x) shifted 5 units right and 2 units down.

It is the graph of g(x) shifted 2 units right and 5 units down.

It is the graph of g(x) shifted 2 units left and 5 units down.

It is the graph of g(x) shifted 5 units left and 2 units down.

If you guys could explain ,I am not sure.

Oct 29, 2018

#1
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The thing that makes x - 5   =  0    tells us the  horizontal translation  = 5  [ positive units to the right ]

The  " -2 "  translates this down 2 units

So...

The parent is translated   5 units to the right and 2  units down

See this graph that confirms this : https://www.desmos.com/calculator/yagdt639xu   Oct 29, 2018
#2
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Is this equation kind of slope intercept form ? but set up a bit different?

jjennylove  Oct 29, 2018
edited by jjennylove  Oct 29, 2018
#3
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See my more complete explanation  in the answer to your  latest  post   CPhill  Oct 29, 2018