Math worksheet focusing on interval notation and domain & range, featuring problems with number lines and spaces for solutions.

Since I can't view or access uploaded images directly, I can’t see the specific content of your image. However, based on the text you've provided, it looks like a Math 10 worksheet on interval notation, domain, and range, with tasks involving:

1. Writing inequalities in interval notation and graphing them.
2. Converting interval notation to inequalities.
3. Interpreting graphs to write interval notation.

Let me walk through each problem based on the structure of what's written. If you provide the exact details (like numbers or symbols), I can give more precise answers. But here’s how to solve each type:

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Part 1: Put in interval notation and draw a graph of each inequality

#### 1. $ x \geq 4 $

- Interval Notation: $[4, \infty)$
- Graph: Draw a number line. Place a closed circle at 4 (since it's "greater than or equal to"), then shade to the right.

#### 2. $ x < 6 $

- Interval Notation: $(-\infty, 6)$
- Graph: Open circle at 6, shade to the left.

#### 3. $ x > -2 $

- Interval Notation: $(-2, \infty)$
- Graph: Open circle at -2, shade to the right.

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Part 2: Write each interval as an inequality

#### 4. $ (-\infty, 8] $

- This means all numbers less than or equal to 8.
- Inequality: $ x \leq 8 $

#### 5. $ [5, \infty) $

- All numbers greater than or equal to 5.
- Inequality: $ x \geq 5 $

#### 6. $ (-2, \infty) $

- All numbers greater than -2.
- Inequality: $ x > -2 $

#### 7. $ [-36, \infty) $

- All numbers greater than or equal to -36.
- Inequality: $ x \geq -36 $

#### 8. $ (-\infty, 6) $

- All numbers less than 6.
- Inequality: $ x < 6 $

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Part 3: Write interval notation that describes the graph

You’ll need to interpret the graph based on:
- Closed circles = included (use bracket `[` or `]`)
- Open circles = not included (use parenthesis `( )`)
- Direction of shading

Let’s assume the graphs are as follows (based on typical problems):

#### 9. Graph: Closed circle at 3, open circle at 9, shaded between.

- So it's from 3 (included) to 9 (not included).
- Interval Notation: $[3, 9)$

#### 10. Graph: Closed circle at 2, open circle at 7, shaded between.

- From 2 (included) to 7 (not included).
- Interval Notation: $[2, 7)$

#### 11. Graph: Open circle at -4, closed circle at 1, shaded between.

- From -4 (not included) to 1 (included).
- Interval Notation: $(-4, 1]$

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $[4, \infty)$ |
| 2 | $(-\infty, 6)$ |
| 3 | $(-2, \infty)$ |
| 4 | $x \leq 8$ |
| 5 | $x \geq 5$ |
| 6 | $x > -2$ |
| 7 | $x \geq -36$ |
| 8 | $x < 6$ |
| 9 | $[3, 9)$ |
| 10 | $[2, 7)$ |
| 11 | $(-4, 1]$ |

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🔍 Tips for Graphing:

- Use closed circles for $\leq$, $\geq$
- Use open circles for $<$, $>$
- Shade in the direction that satisfies the inequality.

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If you can describe the graphs (e.g., "a closed dot at 3, open at 9, shaded in between") or clarify any part, I can adjust the answers accordingly!