# How would you graph y = ln(x-1) +3 without a calculor?

Sep 30, 2016

This is the standard graph of $\ln x$ shifted $+ 1$ unit on the $x$-axis and $+ 3$ units on the $y$-axis

#### Explanation:

Consider the standard function $\ln x$
This can be considered as: $\ln \left(x - a\right) + b$ where $a = b = 0$

The given function $y = \ln \left(x - 1\right) + 3$ is the standard function with two linear transformations: $a = 1$ and $b = 3$

Hence: $y$ is the standard graph of $\ln x$ shifted $+ 1$ unit on the $x$-axis and $+ 3$ units on the $y$-axis

This can be seen the graph of $y = \ln \left(x - 1\right) + 3$ below:

graph{ln(x-1)+3 [-10, 10, -5, 5]}