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 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.
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
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 -------------+----------------+---------