# How do you graph y=lnx-4?

Jul 18, 2018

#### Explanation:

Given: $y = \ln x - 4$

The parent function is $\ln x$. The given function is shifted down by $4$.

Graph of $\ln x - 4$:
graph{ln x - 4 [-10, 10, -10, 5]}

If you don't have a graphing calculator, you can graph the inverse of the parent function $y = {e}^{x}$ and then switch the $x$ and $y$ variables and subtract $4$ from the $y$ value:

$\text{ } y = {e}^{x}$
$\underline{\text{ "x" "|" "y" }}$
$\text{ "-4" "|" } .0183$
$\text{ "0 " "|" } 1$
$\text{ " 1 " "|" } 2.718$
$\text{ "2" "|" } 7.389$
$\text{ "3" "|" } 20.09$

$\text{ } y = \ln x$
$\underline{\text{ "x" "|" "y" }}$
$\text{ ".0183" "|" } - 4$
$\text{ "1 " "|" } 0$
$\text{ " 2.718 " "|" } 1$
$\text{ "7.389" "|" } 2$
$\text{ "20.09" "|" } 3$

$\text{ } y = \ln x - 4$
$\underline{\text{ "x" "|" "y" }}$
$\text{ ".0183" "|" } - 8$
$\text{ "1 " "|" } - 4$
$\text{ " 2.718 " "|" } - 3$
$\text{ "7.389" "|" } - 2$
$\text{ "20.09" "|" } - 1$