Question

Graph y = 3(x + 2)3 - 3 and describe the end behavior.

Answer 1

Can't really graph this for you but I can give you as many specifics as possible.  First of all, that looks like this (to make it more clear): $3(x+2)^3-3$.  It's a third degree function, which is odd.  By definition, one tail goes up and the other one goes down.  Because the leading coefficient is a positive 3, the left tail goes down and the right one goes up.  The "vertex" or point of inflection, is at (-2, -3), which is the parent graph of y = x^3 shifted 2 to the left and down 3.  A few other points on the graph to help you graph it on your own are (-3, -6), (-1, 0), (0, 21), and (1, 78).  Good luck!