Question

How do you graph `y = -1 + log_2x`?

Answer 1

Inverse relation `x = 2 (2^y)` is convenient for making a Table for the graph, for `y=0, +-1, +-2, +-3,...`
`(x, y): ....(1/4, -3) (1/2, -2) (1, -1) (2, 0) (4, 1) (8, 2) (16, 3) ...`
.

Explanation:

Rearrange to the form

`log_2 x=y+1`.

The inverse relation is

`x = 2^(y+1)=2(2^y)>0.`

Now, `(x, y): ....(1/4, -3) (1/2, -2) (1, -1) (2, 0) (4, 1) (8, 2) (16, 3) ...`

The graph cuts x-axis at x = 2.

x-axis, downwards, is the vertical asymptote.

As`x to oo, y to oo`.