MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Let the point (x,y) lie on the curve y=x1 with x=0.
(i) Show that xy=1 for every point on the curve.
(ii) Using the result of part (i), explain why no point of the curve can lie on either coordinate axis.
(iii) Prove that if (x,y) is a point on the curve, then (−x,−y) is also a point on the curve. State the type of symmetry that the graph possesses based on this observation.