The graph of y = f(x) is shown, where the function f is defined by f(x) = ax3 +bx2 + ex +d
and a, b, c, and d are constants. For how many values of x does f(x) = 0?
The function f(x) = ax^3 + bx^2 + ex + d is a polynomial of degree 3. According to the Fundamental Theorem of Algebra, a polynomial of degree n has exactly n complex roots, counting multiplicity.
Since the function f(x) = ax^3 + bx^2 + ex + d can have at most 3 distinct roots, the number of values of x for which f(x) = 0 can be at most 3.