Answer:
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.