MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Let g(x)=x5−4x3+6x2−7.
(i) Determine whether g(x) is even, odd, or neither.
(ii) Identify the term or terms that prevent g(x) from being classified as purely even or purely odd, and justify your answer.
(iii) State the kind of symmetry, if any, that the graph of g(x) will exhibit with respect to the coordinate axes or the origin.