1. ## Graph the function?

I need some help with this one. Thanks in advance

Graph the function.

f(x) = log3(x - 3)

2. Originally Posted by leilani
I need some help with this one. Thanks in advance

Graph the function.

f(x) = log3(x - 3)
When you are trying to graph logs, the easiest way to do it (if you can't use a graphing calculator) is to plot points.

We know that logs are undefined for negative values of x and also for x = 0.

For this particular problem, you should first find the domain and any asymptotes. This will help you decide what x value you should begin with when you start plugging in values.

To find your domain, you need to put the value of the argument $\displaystyle (x-3) > 0$ and solve for x. This gives you x > 3. This is the domain of your log function.

$\displaystyle f(4) = log_3(4-3) = log_3(1) = 0$

Now that one was easy because we know that log(1) = 0. But it gets a little trickier when we are trying logs of other numbers. Just continue plugging values in for x and plot points on your graph. Hope that helps!!

3. Originally Posted by leilani
I need some help with this one. Thanks in advance

Graph the function.

f(x) = log3(x - 3)
Hi there

Your equation has the general form

$\displaystyle f(x) = log(A(x-B))$

where B is the horizontal translation (i.e how much the function is moved left or right across the x axis) and A as a dialation factor (this effects how steep or swallow the function is).

Your function has been moved 3 units to the right and grows at 3 times the rate.

4. Originally Posted by leilani
Graph the function: f(x) = log3(x - 3)
You can either use the definition of logs to graph this log function, or else use the change-of-base formula to convert the function into something your calculator can graph (and for which it can provide you with plot points).

The first way gives:

Code:
-------------+----------------+---------
powers     |    function    | value of
of 3      |    equation    |    y
-------------+----------------+---------
1/3 = 3^(-1) | log_3(1/3) = y |
x = 1/3    | 1/3 = 3^y      |  y = -1
-------------+----------------+---------
1 = 3^(0)  |  log_3(1) = y  |
x = 1      |  1 = 3^y       |  y =  0
-------------+----------------+---------
3 = 3^1    |  log_3(3) = y  |
x = 3      |  3 = 3^y       |  y =  1
-------------+----------------+---------
9 = 3^2    |  log_3(9) = y  |
x = 9      |  9 = 3^y       |  y =  2
-------------+----------------+---------
27 = 3^3    | log_3(27) = y  |
x = 27     | 27 = 3^y       |  y =  3
-------------+----------------+---------
The second way converts "y = log_3(x)" into "y = [ln(x)]/[ln(3)]".