MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
A function p is defined on the closed interval [−4,4]. A detailed verbal description of the graph of p is provided below.
• For −4≤x<−2, the graph is a straight line segment that joins (−4,1) to (−2,−3) and includes both endpoints.
• At x=−2, there is an open circle at (−2,−1).
• For −2<x<1, the graph follows the quadratic curve y=−(x+1)2+2.
• At x=1, the graph has a filled dot at (1,−4) but no other points with x=1.
• For 1<x≤4, the graph is the horizontal line y=−4.
(1) Part 1: (a) Determine all open intervals on which p is continuous.
(2) Part 2: (b) For each value of x at which p is not continuous, classify the discontinuity as removable, jump, or infinite. Support each classification with limit statements based on the described graph.