Question

How do you graph `g(x) = log_3(x - 4)`?

Answer 1

Make a smooth graph that is gently-sloping-down to horizontal through (35/9, -2), (11/3, -1), (5, 0), (7, 1), (13, 2), ( (31, 3),...,(4+3^N, N)... x = 4 ( downwards ) is its vertical asymptote,

Explanation:

The inverse relation for `y = g(x) = log_3 (x-4)` is

`x-4=3^y`.

So, x = 4 + 3^y#.

As `y to -oo, x to 4`. So, x =4 is the vertical asymptote to the graph.

As `x to oo, y to oo, and d/dx(y)=1/(x-4) to 0`.

A short Table for making graph-by-hand, on a rectangular graph paper, is

`(x. y): (35/9, -2), (11/3, -1), (5, 0), (7, 1), (13, 2), (31, 3), ... , (4+3^N, N), ...`