Consider the process of drawing the graph of a polynomial function by plotting a set…
MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Consider the process of drawing the graph of a polynomial function by plotting a set of calculated points.
(i) State any two criteria that should guide the choice of x-values when one prepares a table of values for sketching a polynomial graph.
(ii) The polynomial f(x)=3x4−2x2+1 is to be sketched for −2≤x≤2. Suggest a suitable list of x-values that would allow a clear and accurate sketch, and justify why your choice meets the criteria stated in part (i).
(iii) Explain, with reason, why using unequal step sizes for successive x-values can be advantageous in regions where the graph changes rapidly.