How does the graph of #f(x) = log_2(x - 5) - 2# compare to its parent function f(x) = #log_2 x#?

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Answer 1 · 2015-09-07T13:09:57

#log_2(x-5)-2# is #log_2(x)# shifted down #2# units, and shifted right #5# units.

For any function #f(x)#:

#f(x) + k# is #f(x)# shifted up by #k# units.

#f(x) - k# is #f(x)# shifted down by #k# units.

#f(x+k) # is #f(x)# shifted left by #k# units.

#f(x-k) # is #f(x)# shifted right by #k# units.

From this we can quickly see that #log_2(x-5)-2# is #log_2(x)# shifted down #2# units, and shifted right #5# units.

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