Question

How do you find the domain and range of `y = log_2(x - 3)`?

Answer 1

The argument of a log-function must be positive.

Explanation:

This means `x-3>0->x>3`

If `x` gets closer to `3`, the log will get more and more negative

Or, in the "language""
`lim_(x->3) log_2 (x-3)= -oo`

The other way, `x` getting larger, will get the function larger:
`lim_(x-> oo) log_2 (x-3) = oo`