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 $[-2,0]$
В $[1,5]$
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 graph provided

step 2

From the graph, we observe that $g$ has open circles at the points $(-2, -4)$ and $(3, 3)$, indicating discontinuities at $x = -2$ and $x = 3$

step 3

The closed circles at $(0, 3)$ and $(3, 7)$ indicate that $g$ is continuous at $x = 0$ and $x = 3$

step 4

Therefore, $g$ is continuous in the interval $[-2, 0]$ because there are no discontinuities within this interval

step 5

The interval $[1, 5]$ is not continuous because there is a discontinuity at $x = 3$

Answer

$[-2, 0]$

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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