# How do you graph g(x)=1/2log_3 (x+4)+3?

Aug 6, 2016

Use the inverse relation $x = {9}^{g} / 729 - 4 , , g = 0 , \pm 9 , \pm {9}^{2} , \pm {9}^{3} , \ldots$

#### Explanation:

Inversion:

${3}^{2 g - 6} = x + 4$

$x = {9}^{g} / {9}^{3} - 4 = {9}^{g - 3} - 4$

Now, use the Table for$g = 0 , \pm 9 , \pm {9}^{2} , \pm {9}^{3} , \pm {9}^{4}$

(x, g) = ( 9^(g-3)-4):::... $\left(5 , 4\right) \left(- 2 , 3\right) \left(- \frac{35}{9} , 2\right) \left(- \frac{522}{81} , 1\right)$

$\ldots \to \left(- 4 , - \infty\right)$

oo)#

$x = - 4$ (downwards ) is asymptotic to the graph and $x \succ 4$....