Describe the graph of the function f(x) = x3 − 11x2 + 36x − 36. include the y-intercept, x-intercepts, and the shape of the graph.

y-intercept:  (0, -36); x-intercepts:  (2,0), (3,0), (6,0)

Step-by-step explanation:

Hint:  Please use " ^ " to denote exponentiation:  f(x) = x^3 − 11x^2 + 36x − 36

I guessed that a root of this function is x = 6, with the implication that (x-6) is a factor of f(x) = x^3 − 11x^2 + 36x − 36.  

This can be proven using synthetic division.  The coefficients of the quotient are 2, 3 and 6.  Thus, the x-intercepts are (2,0), (3,0) and (6,0).  Letting x = 0 leaves us with y= -36, so the y-intercept is (0, -36)

The graph begins in Quadrant III, increasing as x increases.  It enters Quadrant I briefly and then it reverses direction and heads downward a bit, and finally turning up and increasing indefinitely in Quadrant I.

35 is an outlier

step-by-step explanation: