The image depicts a triangle plotted on a coordinate plane. To analyze the domain, range, and whether the graph represents a function, let's consider the following:

Domain and Range:

1. Domain: The domain is the set of all possible x-values that the graph covers.

   • From the graph, the x-values range from approximately $x = -5$ to $x = 3$.
   • In set-builder notation, the domain is: $\{ x \mid -5 \leq x \leq 3 \}$

2. Range: The range is the set of all possible y-values that the graph covers.

   • From the graph, the y-values range from approximately $y = -4$ to $y = 5$.
   • In set-builder notation, the range is: $\{ y \mid -4 \leq y \leq 5 \}$

Is it a function?

• A graph represents a function if every x-value (input) corresponds to exactly one y-value (output).
• The given graph fails the vertical line test because there are vertical lines that intersect the graph at more than one point (for instance, around $x = -2$ and $x = 1$).
• Therefore, the graph is not a function. (Answer: No)

Would you like more details or have any questions?

Here are five related questions you might consider:

1. What is the vertical line test, and how does it determine if a graph is a function?
2. How do you find the range and domain of a more complex function?
3. What are some common shapes of graphs that do not represent functions?
4. Can a graph represent a function if the domain or range is restricted to a smaller set?
5. How can transformations (like translations or reflections) affect the domain and range of a graph?

Tip: When determining if a graph is a function, always check if any vertical line intersects the graph at more than one point. This simple test can save time and ensure accuracy.