I also need to know the end-behavior. for example- x----> + or - infinity

There are two ways to solve this problem. The quickest way is to plot the equation and view the end behaviors.

Since we know that the equation given... f(x) = -2(x-4)^3+11 is to the power of 3. The curve will follow the following pattern:

\ /

\____ or ____/

\ /

\ /

After analyzing the graph we can determine the end behavior. If you graph the equation you will find that it follows this pattern:

\

\__(0,0)___

\

\

So as x -> -infinity, y gets bigger and bigger (up), or approaches +infinity

and as x -> +infinity, y goes down or gets bigger and bigger in the negative direction and approaches -infinity

so in all... The steps would be to

1. Determine the power of the function (in english, what number is x raised to).

2. graph the function

3. determine end behavior. (if the line goes up it approaches +infinity, if it goes down it approaches - infinity)

## Comments