How do you graph #y=log_2(x-5)-3#?

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Answer 1 · 2018-02-09T00:14:23

red: #y= log_2#
blue: #y=log_2(x-5)-3#
enter image source here

The point #(x,y)# on the red graph corresponds to the point #(x/d+h, cy+k)# on the blue graph.

#c=1#
#d=1#
#h=5#
#k=-3#

Use the points (1,0), (2,1), (4,2), (8,3) on the original graph (red) to transform it to become the blue graph.

#(1,0) rarr (1/1+5, 1(0)-3) = (6,-3)#

#(2,1) rarr (2/1+5, 1(1)-3) = (7,-2)#

#(4,2) rarr (4/1+5, 1(2)-3) = (9,-1)#

#(8,3) rarr (8/1+5, 1(3)-3) =(13,0)#

Plot the new points accordingly and you will get the blue graph.