1. **State the problem:** We need to find the interval where the function is both increasing and linear. 2. **Analyze the graph description:** The function has three parts: - A curved segment from $x=-8$ to $x=-1$. - A linear segment rising from $x=-1$ to $x=4$. - A linear segment descending from $x=4$ to $x=7$. 3. **Recall definitions:** - A function is **increasing** on an interval if for any $x_1 < x_2$ in that interval, $f(x_1) < f(x_2)$. - A function is **linear** on an interval if its graph is a straight line segment. 4. **Apply to the segments:** - The first segment is curved, so not linear. - The second segment is linear and rising, so it is increasing and linear. - The third segment is linear but descending, so it is not increasing. 5. **Conclusion:** The function is increasing and linear on the interval $$[-1,4]$$. **Final answer:** The function is increasing and linear on the interval $$\boxed{[-1,4]}$$.