The graph of a function satisfies the following conditions on the interval : • The…
MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability
Problem
The graph of a function f satisfies the following conditions on the interval [−2,5]:
• The graph is smooth for x<−2 and for x>5.
• At x=−2 the point (−2,1) is on the graph and there is no break.
• At x=1 the function jumps from f(1−)=2 to f(1+)=−1, and the point (1,−1) is solid.
• At x=3 there is a hole; both one-sided limits equal 4, but f(3) is not defined.
• At x=5 the graph ends with a closed dot at (5,0).
Which of the following lists gives all x-values at which f is not continuous on [−2,5]?
(a) {1}
(b) {1,3}
(c) {1,3,5}
(d) {3}