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

Jun 26, 2016

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

Explanation:

$x \succ 4$ to make log function real.

Rearranging, ${\log}_{2} \left(x + 4\right) = 2 - y$

Inverting, $x + 4 = {2}^{2 - y} = {2}^{2} {2}^{- y} = 4 \left({2}^{- y}\right)$.

So, $x = 4 \left({2}^{- y} - 1\right)$.

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.