How to draw a graph $f(x)=-\log_{3}(3(x-1))$? How to draw a graph $f(x)=-\log_{3}(3(x-1))$?
What's with that 3 before x, should I expose it? so I get $f(x)=-\log_{3}(3(x-1))$?
So how do I then draw it? 
The process (of how I would draw this function):
1.)$f(x)=\log_{3}x$
2.)$f(x)=\log_{3}3x$
3.)$f(x)=\log_{3}(3(x-1))$
4.)$f(x)=-\log_{3}(3(x-1))$
 A: You may want to use the following:


*

*There is a vertical asymptote when the argument of the $\log$ is zero ($x =
   1$).

*The function crosses zero when the argument of the $\log$ is one ($x = 4/3$).

*For large enough $x$, the function behaves like $-\log_3(3x) = -1-\log_3(x)$

A: Usually we draw this kind of elementary functions by mathematical softwares. On the other hand, your process is correct and feasible. It helps understand the rough figure of $f$.
A: Let me give you a summary of what you should do. Firstly you should know that the logarithm function is defined only for positive values. Therefore $3(x-1)>0\rightarrow x>1$. When $f(x)=0$ we have, $3x-3=1\rightarrow x=\frac{4}{3}$. Now we shall consider the derivative of this function. 
$$f'(x)=-\frac{1}{(x-1)\ln 3}$$
$f'(x)<0$ for all $x>1$. 
We also see that, $x\rightarrow \infty\Rightarrow f(x)\rightarrow-\infty$ and when $x\rightarrow 1^+\Rightarrow f'(x)\rightarrow\infty$. 
With all the above information we can draw the graph of $f$ and it turns out like >>this<<. 
