Question

Math

Posted 2 months ago

```
This is the graph of function $g$.
Over which intervals is $g$ continuous?
Choose all answers that apply:
A $[-2,0]$
B $[1,5]$
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 $g$ 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 $(-3, -5)$ and $(3, 3)$, indicating points of discontinuity

step 3

We also observe that there are closed circles at $(-3, 2)$ and $(3, 3)$, indicating that the function is defined at these points

step 4

The interval $[-2, 0]$ does not include any points of discontinuity, so $g$ is continuous over this interval

step 5

The interval $[1, 5]$ includes the point $(3, 3)$, which is a point of discontinuity, so $g$ is not continuous over this interval

step 6

Therefore, the correct answer is $A$ $[-2, 0]$

Answer

A $[-2, 0]$

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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