# How do you graph y=lnx-1?

Sep 22, 2016

The graph of $y$ is the standard function $\ln x$ shifted one unit down the $y -$axis. $y$ has a zero at $x = e$

#### Explanation:

$f \left(x\right) = \ln x$ has a vertical asymtote at $x = 0$ and a zero at $x = 1$

In this question $y = f \left(x\right) - 1$ which simply shifts ("transforms") $f \left(x\right)$ one unit down the $y -$ axis.

To find the zero:

$y = \ln x - 1 = 0 \to \ln x = 1$
$x = {e}^{1} = e$

Hence $y$ has a zero at $x = e$

These features can be seen on the graph of $\ln x - 1$ below:

graph{lnx-1 [-4.64, 15.36, -5.65, 4.35]}