Question

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

Answer 1

This is the standard graph of `lnx` shifted `+1` unit on the `x`-axis and `+3` units on the `y`-axis

Explanation:

Consider the standard function `lnx`
This can be considered as: `ln(x-a)+b` where `a=b=0`

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

Hence: `y` is the standard graph of `lnx` shifted `+1` unit on the `x`-axis and `+3` units on the `y`-axis

This can be seen the graph of `y=ln(x-1)+3` below:

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