Continuity at a Point
Ready, Set, Practice!
If exists and is finite, then is continuous at . True or false? Justify your answer, providing a counterexample if appropriate.
Given a function , whose domain is , we know that and that . Is the function continuous at ? Justify your answer, providing a counterexample if appropriate.
Describe the continuity of the function shown in the graph below.
Determine the domain of the function and verify analytically that it is continuous at , then plot the graph of the function and observe its behaviour in the neighbourhood of . How can you use a graph to check if a function is continuous?
Plot the graph of the function and explain whether it is continuous at .
Find the value of the parameter that makes the piecewise function continuous at . Plot the graph of the continuous function that you have obtained.