MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Consider the two cubic functions g(x)=x3−6x and h(x)=−x3+6x.
(i) For each of x=−3,−2,−1,0,1,2,3, compute the values of g(x) and h(x) and record them in a table.
(ii) Plot the points obtained for both functions on the same pair of axes and draw smooth curves for y=g(x) and y=h(x).
(iii) From your sketch, write the approximate coordinates of the points where the two curves intersect.
(iv) Solve the equation g(x)=h(x) algebraically and compare your algebraic solutions with the graphical estimates from part (iii).
(v) Comment on any symmetry you observe between the graphs of g and h.