Let's analyze the graph provided in the image to determine the domain and range of the function $f$.

Step 1: Domain

The domain represents all the possible values of $x$ (the horizontal axis) for which the function is defined.

• Looking at the graph, the function starts at $x = -3$ and ends at $x = 3$.
• Therefore, the domain is the closed interval $[-3, 3]$.

Step 2: Range

The range represents all the possible values of $y$ (the vertical axis) that the function can take.

• From the graph, the lowest point of the function is at $y = -3$, and the highest point is at $y = 0$.
• Therefore, the range is the closed interval $[-3, 0]$.

Conclusion:

The correct domain is $[-3, 3]$ and the correct range is $[-3, 0]$.

Answer:

Option B: $D = [-3, 3], R = [-3, 0]$.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you determine the domain and range of a function from a graph?
2. What is the difference between open and closed intervals in domain and range?
3. How do domain and range change if a graph is shifted vertically or horizontally?
4. What is the significance of the vertex in a parabola when analyzing its range?
5. Can the domain and range of all functions be determined from their graphs?

Tip: When analyzing the range, always look for the minimum and maximum values of $y$ that the graph reaches.