A polynomial function has a graph that passes through the origin and is symmetric…

MATHEMATICS · Subjective · 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 origin. It intersects the x-axis only at the origin. (i) State whether

f

is even or odd. (ii) Write the simplest polynomial of degree at most 3 that satisfies these properties.