# How do you graph  y=2ln(x+1)?

Nov 21, 2016

y is defined for $x > - 1$ and has a single zero at $x = 0$

#### Explanation:

$y = 2 \ln \left(x + 1\right)$

$\ln \left(x\right)$ is defined for $x > 0$
Hence $y$ is defined for $x > - 1$

$\ln \left(1\right) = 0$
Hence $\ln \left(x + 1\right) = 0$ for $\left(x + 1\right) = 1$
$\therefore y$ has a single zero at $x = 0$

The graph of $y$ is shown below:

graph{2ln(x+1) [-10, 10, -5, 5]}