Final answer:
The polynomial function whose graph passes through (7,11), (11,-10), and (0,3) is x^3 - 18x^2 + 77x - 77.
Step-by-step explanation:
To find a polynomial function that passes through the given points (7,11), (11,-10), and (0,3), we can use the fact that when a polynomial function passes through a point (x,y), the equation of the function can be written as:
(x-a)(x-b)(x-c)... = 0, where a, b, c, etc. are the x-coordinates of the given points.
So, for the given points, the polynomial function can be written as (x-7)(x-11)(x-0) = 0.
Expanding this equation, we get:
x^3 - 18x^2 + 77x - 77 = 0.
Therefore, the polynomial function is f(x) = x^3 - 18x^2 + 77x - 77.