The rate of change of a function is calculated as the change in the dependent variable ($y$) divided by the change in the independent variable ($x$), often called the slope. Using two points from the table, we calculate:

$\text{Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

Step 1: Select Two Points

From the table, let's use the first two points: $(5, 2)$ and $(10, 3)$.

$\Delta y = 3 - 2 = 1$ $\Delta x = 10 - 5 = 5$

Step 2: Compute the Rate of Change

$\text{Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{1}{5} = 0.2$

Thus, the rate of change is 0.2.

Verification with Other Points

To confirm, use $(10, 3)$ and $(15, 4)$: $\Delta y = 4 - 3 = 1, \quad \Delta x = 15 - 10 = 5$ $\text{Rate of Change} = \frac{1}{5} = 0.2$

Similarly, with $(15, 4)$ and $(20, 5)$, the result is the same: $\Delta y = 5 - 4 = 1, \quad \Delta x = 20 - 15 = 5$ $\text{Rate of Change} = \frac{1}{5} = 0.2$

Final Answer:

The rate of change of the function is $\boxed{0.2}$.

Would you like details or have any further questions? Here are 5 related questions for further exploration:

1. How do you interpret the rate of change in real-world contexts?
2. How does the rate of change relate to the slope of a linear graph?
3. Can you use all four points to confirm if the function is linear?
4. What would the graph of this data look like, and how would the slope appear visually?
5. How does a constant rate of change indicate a linear relationship?

Tip: When analyzing tables, ensure that the intervals of the independent variable ($x$) are equal for consistent comparisons of rate of change.