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:
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)