A polynomial function has a graph that passes through the origin and is symmetric…
MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
A polynomial function f has a graph that passes through the origin and is symmetric about the y–axis. The only point where the graph meets the x–axis is the origin and, for large positive or negative x, the values of f(x) are positive.
Answer the following questions.
(i) Is the function f an even function, an odd function, or neither? Give a reason for your answer.
(ii) State the least possible degree of f and justify your answer on the basis of the symmetry and intercept information given.
(iii) Explain how the sign of the leading coefficient can be predicted from the given end–behaviour of the graph.