MATHEMATICS · Single correct · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
The function g(x)=x−1x3−1 is graphed in the window −100≤x≤100, −100≤y≤100. The plotted curve looks smooth and appears to pass through the point (1,3) with no break. Which statement best explains why the graph fails to reveal that g is undefined at x=1?
(a) The calculator connects its plotted points with straight segments, automatically filling any holes in the curve.
(b) Because of round-off error the calculator treats the denominator at x=1 as non-zero, so it plots the limit value and the graph looks continuous.
(c) The pixel resolution is too coarse at that scale to display a single missing point, so the hole is hidden.
(d) Since the factor (x−1) cancels, g simplifies to x2+x+1, so the function is actually defined at x=1.