The question asks for the average rate of change of the function $f(x)$ on the interval $1 \leq x \leq 3$.

The average rate of change of a function over an interval $[a, b]$ is calculated using the formula: $\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$ Here, the interval is $1 \leq x \leq 3$, so $a = 1$ and $b = 3$.

From the graph:

• The value of $f(1)$ appears to be approximately $-8$.
• The value of $f(3)$ appears to be approximately $6$.

Now we can calculate the average rate of change: $\frac{f(3) - f(1)}{3 - 1} = \frac{6 - (-8)}{3 - 1} = \frac{6 + 8}{2} = \frac{14}{2} = 7$

Thus, the average rate of change is $7$.

Would you like more details, or have any questions about this?

Related Questions:

1. How do you interpret the average rate of change in real-life scenarios?
2. How does the average rate of change differ from the instantaneous rate of change?
3. What are the characteristics of functions with a constant average rate of change?
4. How would the average rate of change change if the interval were $1 \leq x \leq 5$?
5. How can you determine concavity or inflection points from the rate of change?

Tip:

To estimate values from a graph more accurately, try identifying key points or using graphing software to enhance precision.