To determine where the function is increasing, decreasing, or constant, let’s analyze the graph:

1. Decreasing Interval: The function starts by decreasing from the left side and reaches its lowest point at $x = -3$.

   • Interval: The function is decreasing on $(-\infty, -3)$.

2. Increasing Interval: After reaching the lowest point, the function begins to increase starting from $x = -3$ and continues to increase towards the right.

   • Interval: The function is increasing on $(-3, \infty)$.

3. Constant Interval: There is no interval where the function remains constant, as it is either increasing or decreasing at all points shown.

Answer:

• Decreasing on: $(-\infty, -3)$
• Increasing on: $(-3, \infty)$
• Constant on: None

Would you like a more detailed explanation of any part?

Here are some related questions for further exploration:

1. What is the significance of the vertex in determining intervals of increase and decrease?
2. How would we find intervals of increase and decrease if given a function equation instead of a graph?
3. How does the slope of the line relate to whether the function is increasing or decreasing?
4. What are other methods for identifying intervals of increase and decrease besides graph analysis?
5. How can we use calculus (derivatives) to confirm intervals of increase and decrease?

Tip: When analyzing functions, always look for key points like maxima, minima, and inflection points, as they help define intervals of increase and decrease.