To estimate the average rate of change from $x = 1$ to $x = 4$, we use the formula for the average rate of change:

$\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$

In this case:

• $x_1 = 1$ and $x_2 = 4$
• From the graph:
  • At $x = 1$, $f(1) \approx 4$
  • At $x = 4$, $f(4) \approx 0$

Now, applying these values into the formula:

$\text{Average Rate of Change} = \frac{f(4) - f(1)}{4 - 1} = \frac{0 - 4}{3} = \frac{-4}{3} \approx -1.3$

Thus, the average rate of change from $x = 1$ to $x = 4$ is approximately $-1.3$.

Would you like more details or further clarification?

Here are 5 related questions:

1. How would the average rate of change differ if we chose different intervals?
2. What is the meaning of a negative average rate of change in this context?
3. How can you determine the instantaneous rate of change at a specific point from a graph?
4. What is the difference between average and instantaneous rates of change?
5. How does the shape of the graph influence the average rate of change over various intervals?

Tip: The steeper the slope between two points, the greater the magnitude of the rate of change.