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.