Sketching a graph of $f(x)$ Given a function $f(x)$ is increasing in the intervals $(-\infty, -1 )$ and $(3, \infty)$, and decreasing in the interval $(-1,3)$ 
If I want to sketch a graph of $f(x)$,  
I know that the maximum point $\implies x=-1$
Minimum Point $\implies x=3$ 
However, let's say given the graph 
$-5<x<5$ 
$-5<y<5$ 
Is there anyway to make the graph nearly accurate from only the given information? 
For example, at which $y$ coordinate point would the maximum and minimum point be at?  Or do I just take a random guess from the given information since I only want to sketch it? 
Here is my sketch - 


Good question. I'll assume your function is of the form $f:\mathbf{R}\to \mathbf{R}$. When you're asked to sketch a function or curve like this, you should just seek to include the information specified. In this case, just draw the graph so that it is increasing on $(-\infty,-1)$ and $(3,\infty)$, while decreasing on $(-1,3)$. Also, draw it so that the maximum point occurs at $x=-1$, and the minimum point occurs at $x=3$. 
If you feel uncomfortable not knowing the $y-$values of your graph at $x=-1,3$, try simply labeling the $y-$value as $y=f(-1)$ and $y=f(3)$, respectively.
EDIT: I just saw your sketch now. That looks fine.
