MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
The polynomial f(x)=2x3−3x2−12x+1 is given.
(a) For x=−3,−2,−1,0,1,2,3,4, prepare a table of values of f(x) and plot the corresponding points to sketch the curve y=f(x).
(b) Using the same set of x-values, calculate the ordinates of −f(x), plot these points on the same axes, and draw the curve y=−f(x).
(c) Describe the relationship you observe between the two curves. Verify your observation algebraically by relating the coordinates of corresponding points on the two graphs.