1. **Problem e)**: Given the domain $\{-2,0,2,3\}$ and range $\{-4,2,1,12,3,4\}$, determine if these sets can represent a function. 2. **Explanation**: A function assigns exactly one output (range value) to each input (domain value). The domain has 4 elements, but the range has 6 elements, which is unusual for a function from this domain. 3. Since the range has more elements than the domain, it suggests multiple outputs for some inputs or extra values not paired with domain elements. 4. Without explicit pairs, we cannot confirm a function. If each domain element maps to exactly one range element, the function is valid. 5. **Problem f)**: Domain and range are both $\mathbb{R}^3$, meaning inputs and outputs are 3D vectors. 6. The top-right scatter plot points are $(-3,-4)$, $(-2,2)$, $(0,1)$, $(1,12)$, $(3,4)$, which are 2D points, not 3D. 7. The bottom-left graph is a parabola opening downward with vertex at approximately $(1,3)$. 8. Since domain and range are $\mathbb{R}^3$, but the graphs show 2D points and a 2D parabola, these do not represent functions from $\mathbb{R}^3$ to $\mathbb{R}^3$. 9. **Summary**: e) The sets given do not clearly define a function without pairing. f) The graphs do not represent functions from $\mathbb{R}^3$ to $\mathbb{R}^3$ as described. Final answers: - e) Not enough information to confirm a function. - f) The graphs do not represent functions from $\mathbb{R}^3$ to $\mathbb{R}^3$.