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From the image you uploaded, the question asks to order the functions \( f(x) \), \( g(x) \), and \( h(x) \) by their **average rates of change** on the interval \( 1 \leq x \leq 3 \), from least to greatest.

### Breakdown of the steps:

1. **Function \( f(x) \)**: You are given the graph of \( f(x) \). To find the average rate of change between \( x = 1 \) and \( x = 3 \), we can calculate it as:
   \[
   \text{Average rate of change of } f(x) = \frac{f(3) - f(1)}{3 - 1}
   \]
   From the graph, you'll need to visually estimate \( f(3) \) and \( f(1) \).

2. **Function \( g(x) \)**: You are given a table for \( g(x) \) with values:
   \[
   g(1) = 32, \quad g(3) = 14
   \]
   The average rate of change of \( g(x) \) is:
   \[
   \frac{g(3) - g(1)}{3 - 1} = \frac{14 - 32}{3 - 1} = \frac{-18}{2} = -9
   \]

3. **Function \( h(x) \)**: The equation for \( h(x) \) is given as:
   \[
   h(x) = -\frac{7}{5}x + 19
   \]
   Since \( h(x) \) is a linear function, its rate of change is constant and equal to the slope, which is \( -\frac{7}{5} \approx -1.4 \).

### Now, let's calculate the average rate of change for \( f(x) \), and then compare all three functions.

Let me estimate the values from the graph for \( f(x) \).The average rate of change for \( f(x) \) on the interval \( 1 \leq x \leq 3 \) is approximately \( 3 \).

### Summary of the average rates of change:
- **\( f(x) \)**: \( 3 \)
- **\( g(x) \)**: \( -9 \)
- **\( h(x) \)**: \( -1.4 \)

### Ordering from least to greatest:
- \( g(x) \) (\( -9 \))
- \( h(x) \) (\( -1.4 \))
- \( f(x) \) (\( 3 \))

If you need further clarification or details, feel free to ask!

Here are 5 questions to deepen your understanding:
1. How do you calculate the average rate of change for a given function over an interval?
2. What does the slope of a linear function tell you about its average rate of change?
3. How can you visually estimate the rate of change from a graph?
4. What are the differences between linear and non-linear functions when calculating the average rate of change?
5. How would changing the interval for \( f(x) \) affect its average rate of change?

**Tip**: When calculating the average rate of change from a graph, always try to pinpoint exact values at the boundaries of the interval for more accuracy.

Order the functions f(x), g(x), and h(x) by their average rates of change on the interval 1 ≤ x ≤ 3, from least to greatest.

Calculate the average rates of change for the functions f(x), g(x), and h(x) on the interval 1 ≤ x ≤ 3, comparing their values. Understand graph interpretation and average rate of change formula in this step-by-step solution for high school students.

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