A function `g` has rule `g(x) = log_e (x -3) + 2`.
- State the maximal domain of `g` and the range of `g` over its maximal domain. (2 marks)
- i. Find the equation of the tangent to the graph of `g` at `(4, 2)`. (2 marks)
ii. On the axes below, sketch the graph of the function `g`, labelling any asymptote with its equation.
Also draw the tangent to the graph of `g` at `(4, 2)`. (4 marks)