https://file.aiquickdraw.com/mathbot/file/17275486889523970xt9j.jpg

The image contains three graphs (labeled 16, 17, and 18), and the task is to write the **domain** and **range** of each graph in both **set-builder** and **interval notation**.

Let's analyze each graph individually:

### Graph 16 (Linear Graph):
- **Type**: This is a straight line extending infinitely in both directions.
- **Domain**: Since the line goes infinitely in both the left and right directions, the domain is all real numbers.
  - Set-builder: \( \{ x \mid x \in \mathbb{R} \} \)
  - Interval notation: \( (-\infty, \infty) \)
- **Range**: The line also extends infinitely up and down, so the range is all real numbers.
  - Set-builder: \( \{ y \mid y \in \mathbb{R} \} \)
  - Interval notation: \( (-\infty, \infty) \)

### Graph 17 (Downward Parabola):
- **Type**: This is a parabola opening downward with its vertex at \( (0, 2) \).
- **Domain**: The parabola extends infinitely to the left and right, so the domain is all real numbers.
  - Set-builder: \( \{ x \mid x \in \mathbb{R} \} \)
  - Interval notation: \( (-\infty, \infty) \)
- **Range**: The highest point of the parabola is \( y = 2 \), and it extends downward infinitely.
  - Set-builder: \( \{ y \mid y \leq 2 \} \)
  - Interval notation: \( (-\infty, 2] \)

### Graph 18 (Cubic or Sinusoidal-like Curve):
- **Type**: This curve appears to be a cubic function or a wave-like function extending indefinitely.
- **Domain**: The curve extends infinitely in both horizontal directions, so the domain is all real numbers.
  - Set-builder: \( \{ x \mid x \in \mathbb{R} \} \)
  - Interval notation: \( (-\infty, \infty) \)
- **Range**: The curve also extends infinitely up and down, so the range is all real numbers.
  - Set-builder: \( \{ y \mid y \in \mathbb{R} \} \)
  - Interval notation: \( (-\infty, \infty) \)

### Summary:
1. **Graph 16**: 
   - Domain: \( (-\infty, \infty) \)
   - Range: \( (-\infty, \infty) \)
2. **Graph 17**: 
   - Domain: \( (-\infty, \infty) \)
   - Range: \( (-\infty, 2] \)
3. **Graph 18**: 
   - Domain: \( (-\infty, \infty) \)
   - Range: \( (-\infty, \infty) \)

Do you need more details or further clarification?

### 5 Questions to Expand Understanding:
1. How would you describe the relationship between domain and range for polynomial functions in general?
2. What is the significance of set-builder notation versus interval notation?
3. How can you determine the range of a function just by looking at its graph?
4. What changes in the domain and range if the parabola in Graph 17 opened upwards instead?
5. How would transformations (like shifts or stretches) affect the domain and range of these graphs?

### Tip:
When identifying the range, always look for the highest and lowest points on the graph to see how far it extends vertically.

Write the domain and range of the graph in set-builder and interval notation for graphs 16, 17, and 18.

Learn how to identify and write the domain and range for different types of graphs, including linear, parabolic, and cubic curves, using set-builder and interval notation. Suitable for Grades 8-10 students.

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