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The image shows a problem where you are asked to determine the domain and range of a circular graph, then check whether the graph represents a function.

### Analysis of the Graph:
The graph appears to show a circle centered at the origin \((0, 0)\), with a radius of 2. This is derived from the circular shape intersecting points along the x- and y-axes at \((-2, 0)\), \((2, 0)\), \((0, -2)\), and \((0, 2)\).

### Domain:
- The domain represents the possible values of \(x\). Since the circle spans from \(-2\) to \(2\) on the x-axis, the domain is:
  \[
  \text{Domain} = [-2, 2]
  \]

### Range:
- The range represents the possible values of \(y\). The circle spans from \(-2\) to \(2\) on the y-axis, so the range is:
  \[
  \text{Range} = [-2, 2]
  \]

### Is it a function?
- To determine if the graph is a function, use the **vertical line test**. If any vertical line intersects the graph at more than one point, the graph does not represent a function. Since a vertical line drawn through the circle would intersect it at two points, the graph **is not a function**.

### Answers for the Problem:
1. The range of the relation: \([-2, 2]\)
2. The domain of the relation: \([-2, 2]\)
3. The graph is **not** the graph of a function because it fails the vertical line test.

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Would you like more details or have any other questions? Here are five related questions for practice:

1. What is the equation of a circle with a radius of 3 centered at \((1, -1)\)?
2. How do you determine the range of a quadratic function like \(y = x^2 - 4\)?
3. What is the domain of the function \(f(x) = \frac{1}{x-3}\)?
4. How does the vertical line test determine if a graph represents a function?
5. What is the difference between the domain and range of a function?

**Tip:** Always check if a graph is a function by using the vertical line test, especially when working with circular or elliptical graphs!

Find the domain and range of the relation shown on the graph. Use the vertical line test to determine whether the graph is the graph of a function.

Analyze the domain, range, and functional properties of a circular graph using the vertical line test. Learn to identify key intervals and determine if the graph represents a function. Ideal for students in Grades 9-11.

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