MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Consider a polynomial function f(x) of degree 3. Answer the following:
(a) Define the terms (a) x-intercept and (b) y-intercept of the graph of a polynomial function.
(b) Without solving any equation, explain why a cubic polynomial can have at most three distinct real x-intercepts.
(c) Give one explicit example of a cubic polynomial that possesses exactly one real x-intercept and another explicit example that possesses exactly three real x-intercepts. Justify, in each case, how your example meets the stated requirement.