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.

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!