To determine the domain and range of the graph and decide whether it represents a function, I'll analyze the provided image.

Domain:

The domain consists of all the possible $x$-values that the graph covers. From the graph:

• The graph stretches horizontally from $x = -6$ to $x = 6$.
• There are no breaks or gaps, so all $x$-values between $-6$ and $6$ are included.

Domain in set-builder notation: $\text{Domain} = \{ x \mid -6 \leq x \leq 6 \}$

Range:

The range consists of all the possible $y$-values that the graph covers. From the graph:

• The lowest point of the graph is at $y = -4$.
• The highest point appears to be at $y = 6$.
• The graph covers all values between these points without any gaps.

Range in set-builder notation: $\text{Range} = \{ y \mid -4 \leq y \leq 6 \}$

Is it a function?

A graph represents a function if, for every $x$-value, there is exactly one corresponding $y$-value.

• This graph does not pass the vertical line test (for example, at $x \approx -4$ and $x \approx 0$, a vertical line would intersect the graph at multiple points), meaning it fails to meet the criteria of a function.

Answer: No, this graph does not represent a function.

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Do you have any further questions or need additional details? Here are some related questions you might consider:

1. What is the vertical line test, and how does it determine whether a graph is a function?
2. How do you find the domain and range for more complex graphs?
3. What is the difference between set-builder notation and interval notation?
4. Can a graph have a domain or range that is not continuous? How does that affect the graph's classification?
5. What are the implications if a graph fails the vertical line test?

Tip: Always use the vertical line test to quickly check if a graph represents a function by observing if any vertical line crosses the graph more than once.