MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Consider the two polynomial functions f(x)=x2−4 and g(x)=x3−4. Answer the following questions about them:
(i) State the domain of each function and give a brief reason for your answer.
(ii) Identify the type of symmetry (even, odd or neither) shown by each function. Justify your answer algebraically.
(iii) Compare the ranges of f and g. Explain why one range is bounded below while the other is not.
(iv) Find all x-intercepts of each graph and comment on the maximum number of such intercepts expected from the degree of the polynomial.