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Let's break down the questions presented in the image and solve them step by step.

### Question 28: Average Rate of Change
The graphs of the functions \( f \), \( g \), and \( h \) are shown, and the task is to analyze the average rate of change over successive intervals \([0, 1]\), \([1, 2]\), \([2, 3]\), and so on.

**Average Rate of Change** for a function \( f(x) \) on the interval \([a, b]\) is given by:
\[
\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}
\]

Let’s analyze the functions:

1. **Function \( f \)**: 
   - This appears to be a straight line, meaning that its slope (rate of change) is constant across all intervals.
   - The rate of change is the same on any interval since it's a linear function.
   
2. **Function \( g \)**: 
   - \( g(x) \) looks like a curve that increases steeply after \( x = 1 \), meaning the rate of change increases as \( x \) increases.
   - The average rate of change over \([0, 1]\) is small, but it gets larger on \([1, 2]\) and even more on \([2, 3]\), reflecting the steepness of the curve.
   
3. **Function \( h \)**: 
   - \( h(x) \) seems to have an initially high rate of change for small \( x \), but this levels off as \( x \) increases.
   - The average rate of change decreases as \( x \) increases, meaning that the function grows more slowly over time.

### Question 29: Changing Water Levels
The problem asks for the **average rate of change** of the water level \( W \) between \( x = 100 \) and \( x = 200 \).

Using the formula for the average rate of change:
\[
\text{Average rate of change} = \frac{W(200) - W(100)}{200 - 100}
\]
To solve this, we would need the values of \( W(100) \) and \( W(200) \) from the graph of \( W(x) \), which is not visible in this portion of the image.

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Do you need further details, or should I clarify any step? Here are five follow-up questions you might consider:

1. How does the shape of a graph relate to the average rate of change over different intervals?
2. Can you find a general formula for the average rate of change for any function?
3. How does the rate of change for a quadratic function differ from that of a linear function?
4. What real-world scenarios could resemble the functions \( f \), \( g \), and \( h \)?
5. How would the average rate of change behave for an exponential function?

**Tip:** The average rate of change gives insight into how fast a function's output is changing over a specific interval—key for understanding trends in both linear and nonlinear systems.

Graphs of the functions f, g, and h are shown. What can you say about the average rate of change of each function on the successive intervals [0, 1], [1, 2], [2, 3], ...?

Explore the average rate of change for functions f, g, and h over successive intervals. Learn how to calculate the rate of change using the formula (f(b) - f(a)) / (b - a), with examples from linear and nonlinear functions. Suitable for Grades 9-11.

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