# How do you graph h(x)=ln(x+1)?

Jan 2, 2017

$h \left(x\right)$ is the standard function $\ln \left(x\right)$ shifted (transformed) one unit left (negative) on the $x$-axis

#### Explanation:

$h \left(x\right) = \ln \left(x + 1\right)$

$\ln \left(x\right)$ is defined for $x > 0 \to h \left(x\right)$ is defined for $x + 1 > 0$
$\therefore h \left(x\right)$ is defined for $x > - 1$

$\ln \left(1\right) = 0 \to h \left(x\right) = 0$ for $x + 1 = 1$
$\therefore h \left(x\right) = 0$ for $x = 0$

$h \left(x\right)$ is the standard function $\ln \left(x\right)$ shifted (transformed) one unit left (negative) on the $x$-axis

The graph of $h \left(x\right)$ is shown below:

graph{ln(x+1) [-10, 10, -5, 5]}