https://file.aiquickdraw.com/mathbot/file/1729034191333r9gq79xe.jpg

In the first image, two graphs show intervals that need to be expressed using interval notation.

### Question 1 (Top Graph)
This graph shows a closed interval from \(1\) to \(3\), inclusive of both endpoints. The blue dots at \(1\) and \(3\) indicate that both endpoints are included.

**Interval Notation:**
\[
[1, 3]
\]

### Question 2 (Bottom Graph)
This graph shows two intervals:
1. An interval from \(-5\) to \(-3\), inclusive of \(-5\) but not \(-3\).
2. Another interval from \(3\) to \(5\), excluding \(3\) but including \(5\).

**Interval Notation:**
\[
[-5, -3) \cup (3, 5]
\]

In this notation, \([ ]\) means the endpoint is included, and \(( )\) means the endpoint is excluded. The symbol \(\cup\) represents the union of two intervals.

Would you like more details or have any questions?

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Here are five related questions to deepen your understanding:

1. What is the difference between open and closed intervals?
2. How would you write the union of two non-overlapping intervals in interval notation?
3. Can an interval extend to infinity, and if so, how is it written?
4. What is the graphical interpretation of a point being included or excluded in an interval?
5. How do you convert inequalities into interval notation?

**Tip:** When writing intervals involving infinity, always use parentheses since infinity itself is never a specific, reachable value.

Write an interval using interval notation to describe the set of values shown on the number lines.

Learn how to use interval notation to describe the set of values from a number line. This problem explains how to write closed and open intervals, as well as how to express unions of intervals, suitable for students in Grades 8-10.

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