How do you graph $y = {log}_{2} (x - 5) - 3$ $y=log_2(x-5)-3$ ?

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Answer 1 · 2018-02-09T00:14:23

red: $y = {log}_{2}$ $y= log_2$
blue: $y = {log}_{2} (x - 5) - 3$ $y=log_2(x-5)-3$
enter image source here

The point $(x, y)$ $(x,y)$ on the red graph corresponds to the point $(\frac{x}{d} + h, c y + k)$ $(x/d+h, cy+k)$ on the blue graph.

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

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

$(1, 0) \to (\frac{1}{1} + 5, 1 (0) - 3) = (6, - 3)$ $(1,0) rarr (1/1+5, 1(0)-3) = (6,-3)$

$(2, 1) \to (\frac{2}{1} + 5, 1 (1) - 3) = (7, - 2)$ $(2,1) rarr (2/1+5, 1(1)-3) = (7,-2)$

$(4, 2) \to (\frac{4}{1} + 5, 1 (2) - 3) = (9, - 1)$ $(4,2) rarr (4/1+5, 1(2)-3) = (9,-1)$

$(8, 3) \to (\frac{8}{1} + 5, 1 (3) - 3) = (13, 0)$ $(8,3) rarr (8/1+5, 1(3)-3) =(13,0)$

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

How do you graph y=log2(x−5)−3y=log_2(x-5)-3?