The curve represented by is known to be symmetric about one of the coordinate axes.
MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
The curve represented by y=x2 is known to be symmetric about one of the coordinate axes.
(i) Explain how the symmetry of a curve can be verified from a set of plotted points.
(ii) For x=−3,−2,−1,0,1,2,3, calculate the corresponding y-values and demonstrate the symmetry for y=x2.
(iii) Describe qualitatively how the value of y changes as ∣x∣ increases, and relate this to the change in the steepness of the graph.