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Multiple Choice
Use the graph of f(x) to determine if the function is continuous or discontinuous at x=c. c=4
A
Continuous
B
Discontinuous
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Verified step by step guidance
1
Identify the point of interest on the graph, which is at x = 4.
Examine the graph at x = 4 to see if there is a break, jump, or hole in the graph. A function is continuous at a point if the graph is unbroken at that point.
Check if the limit of f(x) as x approaches 4 from the left (x -> 4-) is equal to the limit of f(x) as x approaches 4 from the right (x -> 4+).
Determine if the value of the function at x = 4, f(4), is equal to the common limit found in the previous step.
Conclude that the function is discontinuous at x = 4 if there is a break, jump, or if the limits from the left and right do not equal f(4).