# How do you graph k(x) = ln (x + 3) + 6 ?

Mar 8, 2017

Use the parent function $y = \ln \left(x\right)$ and shift it horizontally $3$ to the left ($- 3$) and vertically up $6$

#### Explanation:

The parent function $y = \ln \left(x\right)$ goes through $\left(1 , 0\right)$:

graph{ln x [-7.04, 12.96, -5.36, 4.64]}

Shift it horizontally $3$ to the left $\ln \left(x + 3\right)$ so it goes through $\left(- 2 , 0\right)$ which is an $x$ shift of $- 3$ from $\left(1 , 0\right)$ :
graph{ln (x+3) [-7.04, 12.96, -5.36, 4.64]}

Shift it vertically up $6$, $\ln \left(x + 3\right) + 6$ so $\left(- 2 , 0\right)$ moves up to $\left(- 2 , 6\right)$:
graph{ln(x+3) +6 [-4.58, 15.42, -0.64, 9.36]}