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Question
Math
Posted 2 months ago

This is the graph of function gg.

Over which intervals is gg continuous?

Choose all answers that apply:
A [2,0][-2,0]
B [1,5][1,5]
C None of the above
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Answer from Sia
Posted 2 months ago
Solution by Steps
step 1
To determine the intervals over which the function gg is continuous, we need to analyze the given graph and identify any points of discontinuity
step 2
From the graph, we observe that there are open circles at (3,5)(-3, -5) and (3,3)(3, 3), indicating points of discontinuity
step 3
We also observe that there are closed circles at (3,2)(-3, 2) and (3,3)(3, 3), indicating that the function is defined at these points
step 4
The interval [2,0][-2, 0] does not include any points of discontinuity, so gg is continuous over this interval
step 5
The interval [1,5][1, 5] includes the point (3,3)(3, 3), which is a point of discontinuity, so gg is not continuous over this interval
step 6
Therefore, the correct answer is AA [2,0][-2, 0]
Answer
A [2,0][-2, 0]
Key Concept
Continuity of a function
Explanation
A function is continuous over an interval if there are no points of discontinuity within that interval.

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