Let be a real polynomial function where is a non-negative integer.
MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Let fn(x)=xn be a real polynomial function where n is a non-negative integer.
(i) State the domain of fn.
(ii) Distinguish between the ranges of fn when n is even and when n is odd, giving each in interval notation.
(iii) Explain, with reasoning based on the symmetry of the graph, why the range identified in part (ii) is correct for even n.
(iv) Draw a rough sketch of y=fn(x) for n=2 and for n=3 on the same set of axes and indicate the portions of the y-axis that constitute their ranges.