To determine where the function is increasing, we observe the behavior of the parabola. A function is increasing where its slope is positive, which happens as the graph rises from left to right.

Analysis:

1. The graph of the function is a downward-opening parabola.
2. The function increases as we move from the left side of the graph toward the vertex, then decreases after the vertex.
3. The vertex of the parabola appears at $x = 3$.

Domain of Increasing Behavior:

• The function is increasing on the interval $(-\infty, 3]$.
• It increases up to the vertex at $x = 3$.

Final Answer:

The domain on which the function is increasing is: $(-\infty, 3]$

Let me know if you need further clarification or additional help!

Here are some related questions to expand your understanding:

1. How do you find the vertex of a parabola given its equation?
2. What is the domain where the function is decreasing?
3. How do you identify intervals of increasing/decreasing behavior from a graph?
4. What is the role of the derivative in determining increasing and decreasing intervals?
5. How does the direction of the parabola (upward/downward) affect its increasing intervals?

Tip: The vertex of a parabola is the key point where the function transitions between increasing and decreasing behavior.