SOLUTION: Find the intervals on which the function is increasing, and on which the function is decreasing. Here is the graph and other parts of the question I am not positive about: http

Algebra ->  Functions -> SOLUTION: Find the intervals on which the function is increasing, and on which the function is decreasing. Here is the graph and other parts of the question I am not positive about: http      Log On


   

Question 905910: Find the intervals on which the function is increasing, and on which the function is decreasing.
Here is the graph and other parts of the question I am not positive about:
http://i.imgur.com/mruKsFU.png
My answers:
For decreasing: [-3,0] U [2,∞)
For increasing: (-∞,∞)

I am confused on all this.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
You are a bit confused, so let's see if we can straighten you out.




It is unfortunate that the people who made mathematics gave open 
intervals and points the same kind of notation.  A point has an
x-value and a y-value, but an interval has two x-values.

So be EXTREMELY careful to notice the difference between the point
(a,b) and the interval (a,b), in the following:

From negative infinity to the point (-3,-2) the graph is falling, so it
is decreasing from x = negative infinity to x = -3.

So the graph is DECREASING on the interval (-oo,-3).  

From the point (-3,-2) to the point (0,4) the graph is rising, so it
is increasing from x=-3 to x=0

So the graph is INCREASING on the interval (-2,0).

From the point (0,4) to the point (2,1) the graph is falling again,
so it is decreasing again from x=0 to x=2.

So the graph is DECREASING on the interval (0,2).

From the point (2,1) to positive infinity the graph is rising,
so it is increasing from x=2 to x=oo

So the graph is INCREASING on the interval (2,oo)

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Answer: increasing on the intervals (-3,0) and (2,oo).
        decreasing on the intervals (-oo,-3) and (0,2).

Edwin