Choose the correct interval notation for the graph. (You get only one try for the answer; be careful.)

Interval Notation

(-∞, -3] ⋃ [3,7)

(-∞, -3) ⋃ (3,7)

[-∞, -3) ⋃ [-3,7]

(-∞, -3) ⋃ [3, 7]
None of these

To determine the correct interval notation for the graph, we need to interpret the notation provided:

1. \((-∞, -3] ⋃ [3,7)\)
2. \((-∞, -3) ⋃ (3,7)\)
3. \([-∞, -3) ⋃ [-3,7]\)
4. \((-∞, -3) ⋃ [3, 7]\)
5. None of these

Here’s a quick review of interval notation:

- \((-∞, a)\): All numbers less than \(a\), not including \(a\).
- \((-∞, a]\): All numbers less than or equal to \(a\), including \(a\).
- \((a, b)\): All numbers between \(a\) and \(b\), not including \(a\) or \(b\).
- \([a, b)\): All numbers between \(a\) and \(b\), including \(a\) but not \(b\).
- \([a, b]\): All numbers between \(a\) and \(b\), including both \(a\) and \(b\).

Considering each option:

1. \((-∞, -3] ⋃ [3,7)\) includes all numbers less than or equal to \(-3\) and all numbers from \(3\) to \(7\), including \(3\) but not \(7\).
2. \((-∞, -3) ⋃ (3,7)\) includes all numbers less than \(-3\) and all numbers from \(3\) to \(7\), not including \(3\) or \(7\).
3. \([-∞, -3) ⋃ [-3,7]\) is incorrect because \([-∞, -3)\) is not a proper interval notation.
4. \((-∞, -3) ⋃ [3, 7]\) includes all numbers less than \(-3\) and all numbers from \(3\) to \(7\), including \(3\) and \(7\).

If we visualize these on a number line, it becomes clearer which intervals include the boundary points:

- If \(-3\) is included (closed interval at \(-3\)), then we must have \(-∞, -3]\).
- If \(3\) is included (closed interval at \(3\)), then we must have \([3,\).

So, the correct choice based on typical interval conventions would be the one that includes these specific boundaries correctly.

Considering the provided intervals:

- \((-∞, -3] ⋃ [3,7)\) includes \(-3\) and excludes \(7\), which might match common graphing conventions.

Therefore, the correct interval notation for the graph is:

**(-∞, -3] ⋃ [3,7)**.

Do you want details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you determine whether to use a square bracket or a parenthesis in interval notation?
2. Can you explain the difference between an open interval and a closed interval?
3. How would you represent the interval where all numbers between -5 and 5 are included, but not -5 and 5 themselves?
4. What is the union of the intervals \([1, 4]\) and \((3, 5]\)?
5. How can interval notation be used to describe the domain of a function?

**Tip:** Always sketch a number line when working with interval notation to visually confirm which points are included or excluded.

Choose the correct interval notation for the graph. (You get only one try for the answer; be careful.)

Interval Notation:

1. (-∞, -3] ⋃ [3,7)
2. (-∞, -3) ⋃ (3,7)
3. [-∞, -3) ⋃ [-3,7]
4. (-∞, -3) ⋃ [3, 7]
5. None of these

This math problem requires choosing the correct interval notation for a graph. The options involve open and closed intervals such as (-∞, -3] ⋃ [3,7). Learn how to properly use interval notation and understand how to express different sections of a number line. Suitable for students in Grades 9-12.

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