MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Let p(x)=2x3−5x+1 and q(x)=−3x4+2. Use these expressions to answer the following:
(i) Calculate the y-intercept of each polynomial.
(ii) Determine which of the two functions grows faster in magnitude as ∣x∣ becomes very large. Support your answer by referring to suitable algebraic features of the polynomials.
(iii) Evaluate p(2) and q(2), then state which value is larger. Explain briefly why this comparison at x=2 does or does not agree with your conclusion in part (ii).