MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
A function g is described below. For every portion, straight line segments join consecutive points unless stated otherwise.
• A closed circle at (−3,−1); the graph then follows a straight line to an open circle at (0,2).
• There is no point of the graph at (0,2). Instead, a closed circle is placed at (0,1) and the graph proceeds horizontally to an open circle at (3,1).
• The only point of the graph having x=3 is a closed circle at (3,4). From there, the graph follows a straight line to a closed circle at (5,0).
Using this description, answer the following.
(i) Neatly sketch the graph of g on your answer sheet, marking every closed and open circle exactly as specified.
(ii) Identify all points in the domain [−3,5] where g is not continuous. For each such point, state the type of discontinuity and justify your classification with reference to left-hand limit, right-hand limit and function value.
(iii) Comment on the continuity of g at the end-points x=−3 and x=5 according to the definition of continuity on a closed interval.