1. **Problem Statement:** We are given the volume of a cube as a function of its side length $s$: $$V = s^3$$ 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 with side length $s$ is calculated by cubing the side length: $$V = s^3$$ This means for any value of $s$, we raise it to the power of 3 to find $V$. 3. **Table of Values:** Let's calculate $V$ for some values of $s$, including negative, zero, and positive values: | $s$ | $V = s^3$ | |-----|-----------| | -2 | $(-2)^3 = -8$ | | -1 | $(-1)^3 = -1$ | | 0 | $0^3 = 0$ | | 1 | $1^3 = 1$ | | 2 | $2^3 = 8$ | 4. **Graph Sketch Explanation:** The graph of $V = s^3$ is a cubic curve that passes through the origin $(0,0)$. - For positive $s$, $V$ increases rapidly. - For negative $s$, $V$ decreases rapidly in the negative direction. - The curve has an S-shape, typical of cubic functions. 5. **Why Include Negative Inputs?** Including negative inputs helps us understand the behavior of the function for all real numbers, not just positive ones. It shows the symmetry and the nature of the cubic function, which unlike even powers, produces negative outputs for negative inputs. 6. **Linearity of the Graph:** The graph is **non-linear** because the relationship between $s$ and $V$ is cubic, not a straight line. The S-shaped curve confirms this non-linearity, as linear functions produce straight lines. **Final Answer:** The function $V = s^3$ produces an S-shaped cubic curve that is non-linear, passes through the origin, and includes both positive and negative values of $s$ to fully describe its behavior.