SOLUTION: Find the domain and range of the graph of each function. y=log2(x-3) (2 is the base of the log) WE were told that the answer would involve inf. -inf or xero

Algebra.Com
Question 71811: Find the domain and range of the graph of each function. y=log2(x-3)
(2 is the base of the log) WE were told that the answer would involve inf. -inf or xero
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Find the domain and range of the graph of each function. y=log2(x-3)
(2 is the base of the log)
-------------------
y=log2(x) has domain (0,inf) and range (-inf,inf)
But you have y=log2(x-3):
The x-3 moves the x values 3 to the right and leaves the y values as they were.
So, domain is (3,inf) and range is (-inf,inf).
=========
Cheers,
Stan H.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Find the domain and range of the graph of each function. 
y=log2(x-3). WE were told that the answer would involve 
inf. -inf or zero

Only logarithms of positive numbers are defined.   Therefore log2(x-3) 
is only defined when x-3 is positive, or

                          x - 3 > 0
                              x > 3

So the domain is (3, ¥)

Plot the graph by y = log2(x-3) getting some points, say

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

  

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



So the range (the set of possible y-values) contains all real 
values and is thus (-¥, ¥)

Edwin
RELATED QUESTIONS

How do I find the y intercept, x intercept, range, and domain of the following function: (answered by lwsshak3)
What is the domain, range, x-intercept and vertical asymptote of the function: log[base (answered by jsmallt9)
Find the domain and range of each function.... (answered by richwmiller)
Graph. Find the domain and range of each function. Show me step by step please.... (answered by stanbon)
Find the domain and range of: f(x)=8+6*log base 9... (answered by stanbon)
How would find the domain and range of this function: y=3 log x ? Thank you very much! (answered by lwsshak3)
7. Sketch graph of each function and state the domain and range y= (x)-4 (answered by mersha)
Thank you for your help! Sketch each function. State the domain, range, values of... (answered by Fombitz)