Which is the graph of the function f(x) = x3 + 6x2 + 11x + 6?

f(x) = x^3 + 6x2 + 11x + 6 begins with a positive 3rd power of x.  Immediately we know that the graph begins in Quadrant 3 and continues (not ends) in Quadrant 1.  Looking at the last term, we see that possible factors may be 6, 3, 2 or 1 or one or more of the negatives.  Supposing I chose -2 and test whether it is or is not a root of this function:

      _____________
-2  /   1   6   11    6
              -2   -8   -6
      ----------------------
         1    4    3    0

Because the remainder here is zero, we know that -2 is a root.  Thus, the graph passes thru (-2,0).  From the coefficients 1 4 3, we see that -1 and -3 are the other roots.  The graph crosses the x-axis at x = -1, x= -3 and x= -2.
Can you now identify the graph that properly represents  f(x) = x3 + 6x2 + 11x + 6?

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