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.
So you would probably want to start with x=4 to find points on your graph.
$\displaystyle f(4) = log_3(4-3) = log_3(1) = 0$
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!!
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.
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:
The second way converts "y = log_3(x)" into "y = [ln(x)]/[ln(3)]".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 -------------+----------------+---------