How do you graph #y = 2-log_(2)(x+4)#?

1 Answer
Jun 26, 2016

Use the inverse relation #x=4(2^(-y)-1)#. Form a Table #{(x, y)}, y=0, +-1, +-2, +-3,...# and make a graph smoothly, through these points. #x=-4# gives the vertical asymptote and #x> -4#...

Explanation:

#x>-4# to make log function real.

Rearranging, #log_2 (x+4)=2-y#

Inverting, #x+4=2^(2-y)=2^2 2^(-y)=4( 2^(-y))#.

So, #x=4(2^(-y)-1)#.

Sample data for making a graph:

(x, y): (124, 5) (60, -4) (28, -3) (12, -2) (4, -1) (0, 0)

      (-2, 1) (-3, 2) (-7/2, 3) (-15/4, 4) (-31/8, -5)

#x=-4# gives the vertical asymptote.