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The given graph appears to be a curve. Let's analyze whether this relation is a function and determine its domain and range.

### Step 1: Determine if it is a function
To check if a relation is a function, we apply the **vertical line test**. This test states that if any vertical line intersects the graph more than once, the relation is not a function. If every vertical line intersects the graph at most once, the relation is a function.

From the graph:
- Any vertical line drawn across the curve will intersect the graph at only one point.

Thus, the graph **passes the vertical line test**, meaning the relation **is a function**.

### Step 2: Domain
The **domain** of a function is the set of all possible input values (x-values) for which the function is defined.

- From the graph, the function exists for all values of \( x \) starting from approximately \( x = -2 \) and continues indefinitely to the right. 
- Thus, the domain is \( x \in [-2, \infty) \).

### Step 3: Range
The **range** of a function is the set of all possible output values (y-values).

- The graph starts from \( y = -6 \) and extends upwards without bound.
- Therefore, the range is \( y \in [-6, \infty) \).

### Summary:
- **Relation**: This is a function.
- **Domain**: \( x \in [-2, \infty) \)
- **Range**: \( y \in [-6, \infty) \)

Would you like further clarification, or do you have any questions? Here are five related questions to expand on this concept:

1. What is the significance of the vertical line test in determining if a relation is a function?
2. How would the domain change if the curve were shifted horizontally?
3. Can a function have a range that is bounded above but not below?
4. What happens to the function if the curve is reflected across the x-axis?
5. How does the concept of one-to-one functions relate to this graph?

**Tip:** Always check for horizontal asymptotes or breaks in the graph when determining the range, especially when the curve approaches infinity.

Determine whether each relation is a function, and state its domain and range.

Learn how to determine whether a relation is a function using the vertical line test and how to find its domain and range from the graph. Suitable for students in Grades 9-11.

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