MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Two polynomial functions are given by F(x)=3x5−x3+2x and G(x)=−2x6+4x4−x2+7.
(i) State the degree and leading coefficient of each polynomial.
(ii) Without plotting, explain which polynomial attains larger magnitude for sufficiently large positive values of x, and which dominates for sufficiently large negative values of x.
(iii) Determine for each polynomial whether it is even, odd, or neither, providing justification.
(iv) Using only the leading terms, indicate which of F(x) or G(x) is positive for all sufficiently large positive x. Explain your reasoning clearly.