1. **Problem Statement:** We are given the volume of a cube as a function of its side length $s$, defined by the equation $$V = s^3$$. We need to create a table of values, sketch the graph, explain the inclusion of negative inputs, and describe the graph's linearity. 2. **Formula and Explanation:** The volume $V$ of a cube is calculated by cubing the side length $s$. This means for any value of $s$, $$V = s^3$$. Important to note is that cubing a negative number results in a negative volume, which is mathematically consistent but physically may not represent a real cube. 3. **a. Table of Values:** | Side length $s$ | Volume $V = s^3$ | |-----------------|-----------------| | -2 | $(-2)^3 = -8$ | | -1 | $(-1)^3 = -1$ | | 0 | $0^3 = 0$ | | 1 | $1^3 = 1$ | | 2 | $2^3 = 8$ | 4. **b. Sketching the Graph:** The graph of $V = s^3$ is a cubic curve passing through the points from the table: (-2, -8), (-1, -1), (0, 0), (1, 1), and (2, 8). It is symmetric about the origin, rising steeply for positive $s$ and falling steeply for negative $s$. 5. **c. Importance of Negative Inputs:** Including negative inputs helps us understand the behavior of the cubic function for all real numbers. It shows that the function is odd and symmetric about the origin, meaning $V(-s) = -V(s)$. This symmetry is important in understanding the full shape of the graph. 6. **d. Linearity of the Graph:** The graph is non-linear because the relationship between $s$ and $V$ is cubic, not a straight line. The curve bends and changes slope, reflecting the cubic growth rate rather than a constant rate of change. **Final Answer:** The function $V = s^3$ produces a cubic curve that is non-linear and symmetric about the origin, with volume values increasing steeply for positive side lengths and decreasing steeply for negative side lengths.