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To determine where the function \( f(x) \) is increasing or decreasing from the graph, we can observe the behavior of the function as \( x \) increases:

1. **Decreasing Interval**: From the leftmost part of the graph until the lowest point of the vertex, the function \( f(x) \) is decreasing. The \( x \)-coordinates for this part appear to start from around \( x = -2 \) and continue until \( x = 0 \). This can be interpreted as the function decreasing as \( x \) increases within this interval. Thus, the decreasing interval is \( x \in (-\infty, 0) \).

2. **Increasing Interval**: From the vertex moving towards the right, the function begins to increase. The increase starts at \( x = 0 \) and continues as \( x \) moves further to the right. The \( x \)-coordinates for this part appear to end around \( x = 2 \), and the function continues to increase even beyond this point. Therefore, the increasing interval is \( x \in [0, \infty) \).

To summarize:
- **Decreasing**: \( (-\infty, 0) \)
- **Increasing**: \( [0, \infty) \)

If you have any questions or need further details, feel free to ask!

Here are some related questions you might consider:
1. What is the vertex of this parabola and what does it signify?
2. How can you determine the exact coordinates of the vertex from a graph?
3. What might the equation of this parabola look like based on the graph?
4. How does the concept of the derivative help in finding increasing and decreasing intervals analytically?
5. Can you explain the first and second derivative tests and how they apply to graphs like this?

**Tip**: When trying to determine intervals of increase and decrease graphically, look for where the function's slope changes from positive to negative or vice versa; these points often indicate local minima or maxima.

Determine where the function f(x) is increasing and/or decreasing based on the graph.

Learn how to determine where a function is increasing and decreasing based on a graph. This problem involves identifying intervals of increase and decrease for a given function, suitable for students in Grades 8-10.

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