https://file.aiquickdraw.com/mathbot/file/17296262159013gv1k717.jpg

Let's analyze the two graphs in the image to determine the domain, range, and whether or not the graph represents a function.

### Graph 2
- **Graph Description**: The curve is a sideways parabola, indicating that it fails the vertical line test (i.e., a vertical line crosses the curve at more than one point).
- **Domain**: The graph extends horizontally between \( x = -5 \) and \( x = 5 \), so the domain is:
  \[
  -5 \leq x \leq 5
  \]
- **Range**: The graph extends vertically between \( y = -5 \) and \( y = 5 \), so the range is:
  \[
  -5 \leq y \leq 5
  \]
- **Is it a function?**: No. Since the graph fails the vertical line test, it is not a function. (Correct as written in your sheet.)

### Graph 3
- **Graph Description**: The curve is a regular parabola opening downwards. It passes the vertical line test, meaning it is a function.
- **Domain**: The parabola extends horizontally without bounds, so the domain is:
  \[
  (-\infty, \infty)
  \]
- **Range**: The highest point of the graph is \( y = 0 \) (the vertex), and the graph extends downward to \( y = -5 \), so the range is:
  \[
  -5 \leq y \leq 0
  \]
- **Is it a function?**: Yes, it passes the vertical line test.

Would you like more details on any of these answers or further clarification?

### Related Questions:
1. Why does failing the vertical line test make a graph not a function?
2. What happens to the domain and range when a parabola opens sideways instead of upwards or downwards?
3. How would the graph of a quadratic function change if its vertex was moved?
4. Can a function have a range that extends infinitely?
5. How can you modify the domain or range of a function by restricting the graph?

### Tip:
When checking if a graph represents a function, always apply the vertical line test. If any vertical line crosses the graph more than once, it is **not** a function!

Analyze the domain, range, and function status for two given graphs: a sideways parabola and a regular parabola.

This problem involves analyzing two graphs to determine their domain, range, and whether they represent functions. It covers key algebraic concepts, including the vertical line test, domain and range, and parabolas, suitable for students in Grades 8-10.

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