Question

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

Answer 1

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.