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

1 Answer
Feb 9, 2018

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

Explanation:

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.