MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Let q(x)=3x4−4x3+x2−6. Study the graph of q(x) by answering the following:
(i) Verify, by direct substitution, that q(x) is neither an even function nor an odd function.
(ii) Explain why the leading term alone is sufficient to determine x→±∞limq(x), and then find these two limits.
(iii) On the basis of parts (i) and (ii), construct a labelled qualitative sketch of the graph, indicating its end behaviour and the approximate position of its intercepts with the coordinate axes.