From the graph you've provided, the function appears to be a segment of a parabola with endpoints on the x-axis. Based on this, we can determine the domain and range.

Domain:

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

• The function starts at $x = -4$ and ends at $x = 4$.
• At $x = -4$, the graph has an open circle, which means $-4$ is not included in the domain.
• At $x = 4$, the graph has a closed circle, so 4 is included.

Thus, the domain in interval notation is: $(-4, 4]$

Range:

The range is the set of all possible y-values. From the graph:

• The lowest point of the function is at $y = -2$.
• The highest points of the function are at $y = 1$.
• At $y = 1$, the graph has an open circle on the left and a closed circle on the right.

Thus, the range in interval notation is: $[-2, 1)$

Summary:

• Domain: $(-4, 4]$
• Range: $[-2, 1)$

Do you want further details or have any questions?

Here are some related questions for practice:

1. What is the difference between open and closed intervals in domain and range?
2. How can we find the vertex of a parabola from its graph?
3. How would the domain change if both endpoints were open circles?
4. How do we find the equation of the function given its graph?
5. What is the significance of symmetry in a parabola’s graph?

Tip: Always check whether the endpoints of a function are open or closed to determine if they are included in the domain or range!