Let's analyze each relation step by step: --- ### Relation 1 **Step 1: Check if each domain element maps to exactly one range element.** - Sky → 0 - Pen → 0 - Desk → 0 - Pencil → 0 - Paper → -9 **Explanation:** Every domain element is mapped to exactly one range element with no repeats or ambiguity. **Step 2: Decide if it is a function.** Since each input (domain) has exactly one output (range), **Relation 1 is a function.** --- ### Relation 2 **Step 1: Check if each domain element maps to exactly one range element.** - -9 → 7 - 0 → 0 - 4 → 7, 0 (maps to two different values) - 9 → 3 **Explanation:** The domain value "4" maps to both 7 and 0, which means one input gives two outputs. **Step 2: Decide if it is a function.** Since at least one input maps to more than one output, **Relation 2 is NOT a function.** --- ### Relation 3 **Step 1: Check the ordered pairs.** - (h, z), (w, h), (e, h), (z, z) **Explanation:** Each first element (input) is unique: h, w, e, z. No input repeats. **Step 2: Decide if it is a function.** Since each input has only one output, **Relation 3 is a function.** --- ### Relation 4 **Step 1: Check the ordered pairs.** - (7, n), (0, n), (4, n), (-3, n) **Explanation:** Each first element (input) is unique: 7, 0, 4, -3. No input repeats. **Step 2: Decide if it is a function.** Since each input has only one output, **Relation 4 is a function.** --- ## Final Answers - **Relation 1:** Function - **Relation 2:** Not a function - **Relation 3:** Function - **Relation 4:** Function

Let's analyze each relation based on the provided image step by step: --- ### Relation 1 (from the image): **Step 1:** Check if each domain element maps to exactly one range element. - Sky → 0 - Pen → 0 - Desk → 0 - Pencil → 0 - Paper → -9 **Explanation:** Each domain element (Sky, Pen, Desk, Pencil, Paper) maps to exactly one range element. No element maps to multiple values. **Step 2:** Since each input maps to only one output, **Relation 1 is a function.** --- ### Relation 2 (from the image): **Step 1:** Check the mappings: - -9 → 7 - 0 → 0 - 4 → 7, 0 (maps to two different outputs) - 9 → 3 **Explanation:** The input 4 maps to both 7 and 0, which violates the rule of a function (each input should map to only one output). **Step 2:** Since at least one input maps to multiple outputs, **Relation 2 is NOT a function.** --- ### Relation 3 (from the image): **Step 1:** List the pairs: - (h, z) - (w, h) - (e, h) - (z, z) **Explanation:** All domain elements (h, w, e, z) are unique and map to only one value each. **Step 2:** Since each input has exactly one output, **Relation 3 is a function.** --- ### Relation 4 (from the image): **Step 1:** List the pairs: - (7, n) - (0, n) - (4, n) - (-3, n) **Explanation:** All domain elements are unique and map to only one value. **Step 2:** Since each input maps to only one output, **Relation 4 is a function.** --- ## Final Summary: | Relation | Is it a function? | |------------|-------------------| | Relation 1 | Yes | | Relation 2 | No | | Relation 3 | Yes | | Relation 4 | Yes | **Final Answer:** Relations 1, 3, and 4 are functions; Relation 2 is not.