the graph of the function f is shown above. on which of the following intervals is f continuous? (a) (-1,1)…
the graph of the function f is shown above. on which of the following intervals is f continuous? (a) (-1,1) (b) (1,2) (c) (2,3) (d) (3,5)
Answer
Explanation:
Step1: Recall continuity definition
A function is continuous on an interval if there are no breaks, jumps, or holes in the graph on that interval.
Step2: Analyze interval (-1,1)
There is a vertical - asymptote in the interval (-1,1), so the function is not continuous there.
Step3: Analyze interval (1,2)
There is a hole in the graph at (x = 2) and a point - discontinuity at (x=1), so the function is not continuous on (1,2).
Step4: Analyze interval (2,3)
There is a jump - discontinuity at (x = 2), so the function is not continuous on (2,3).
Step5: Analyze interval (3,5)
The graph has no breaks, jumps, or holes in the open interval (3,5), so the function is continuous on (3,5).
Answer:
D. (3,5)