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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]

В [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 graph provided
step 2
From the graph, we observe that gg has open circles at the points (2,4)(-2, -4) and (3,3)(3, 3), indicating discontinuities at x=2x = -2 and x=3x = 3
step 3
The closed circles at (0,3)(0, 3) and (3,7)(3, 7) indicate that gg is continuous at x=0x = 0 and x=3x = 3
step 4
Therefore, gg is continuous in the interval [2,0][-2, 0] because there are no discontinuities within this interval
step 5
The interval [1,5][1, 5] is not continuous because there is a discontinuity at x=3x = 3
Answer
[2,0][-2, 0]
Key Concept
Continuity of a function
Explanation
A function is continuous over an interval if there are no breaks, jumps, or holes in the graph within that interval.

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