To analyze the graph:

1. Domain:

The domain of a graph is the set of all possible $x$-values (inputs) for which the graph has points.

Domain in Set-Builder Notation: $\{ x \mid -4 \leq x \leq 6 \}$ The graph extends horizontally from $x = -4$ to $x = 6$.

2. Range:

The range of a graph is the set of all possible $y$-values (outputs) for which the graph has points.

Range in Set-Builder Notation: $\{ y \mid -2 \leq y \leq 5 \}$ The graph extends vertically from $y = -2$ to $y = 5$.

3. Is the graph a function?

A graph represents a function if, for every $x$-value, there is at most one corresponding $y$-value. In other words, it must pass the vertical line test.

Answer: No, the graph is not a function, because there are $x$-values where a vertical line would intersect the graph at more than one point (e.g., at $x = -1$).

Would you like more details or have any questions?

Related Questions:

1. How do you determine the domain of more complex graphs?
2. What methods can be used to determine if a graph is a function?
3. How would the domain and range change if the triangle were moved upward?
4. What is the significance of the range in real-world applications?
5. Can a shape with curves, like a circle, be a function?

Tip:

Always check if the graph passes the vertical line test to determine if it represents a function.