Question 71811
<pre><font size = 4><b>Find the domain and range of the graph of each function. 
y=log<sub>2</sub>(x-3). WE were told that the answer would involve 
inf. -inf or zero

Only logarithms of positive numbers are defined.   Therefore log<sub>2</sub>(x-3) 
is only defined when x-3 is positive, or

                          x - 3 > 0
                              x > 3

So the domain is (3, <font face = "symbol">¥</font>)

Plot the graph by y = log<sub>2</sub>(x-3) getting some points, say

(4,0), (5,1), (7,2), (11,3) (3.25, -2)

{{{ graph(300, 300, -3, 12, -11, 4, ln(x-3)/ln(2))}}}  

The vertical line (drawn in green below) has equation x = 3 
and it is an asymptote:

{{{ graph(300, 300, -3, 12, -11, 4, ln(x-3)/ln(2), 999(x-3))}}}

So the range (the set of possible y-values) contains all real 
values and is thus (-<font face = "symbol">¥</font>, <font face = "symbol">¥</font>)

Edwin</pre>