Functions $$ 1 \leftarrow \quad $$ State the domain and range for the following relation. Then determine whether the relation represents a function. $$ \{(5,4),(-2,4),(7,5),(5,13)\} $$ Part 1 of 3

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Sure! Let's break down the problem step by step.

### Given Relation:
$$
\{(5, 4),\ (-2, 4),\ (7, 5),\ (5, 13)\}
$$

### 1. **Domain**
The **domain** of a relation consists of all the **first elements** (inputs) in each ordered pair.

- **First elements**: $$5, -2, 7, 5$$

Since sets do not include duplicate elements, we list each unique input once.

- **Domain**: $$\{ -2,\ 5,\ 7 \}$$

### 2. **Range**
The **range** of a relation consists of all the **second elements** (outputs) in each ordered pair.

- **Second elements**: $$4, 4, 5, 13$$

Again, listing each unique output once.

- **Range**: $$\{ 4,\ 5,\ 13 \}$$

### 3. **Determining if the Relation is a Function**
A **function** is a special type of relation where **each input is associated with exactly one output**. In other words, no two ordered pairs should have the same first element paired with different second elements.

Let's examine the given relation:

- $$5$$ is paired with **4** in $$(5, 4)$$
- $$5$$ is also paired with **13** in $$(5, 13)$$

Here, the input $$5$$ is associated with **two different outputs** ($$4$$ and $$13$$). This violates the definition of a function.

- **Conclusion**: The relation **does not** represent a function.

### **Summary**
- **Domain**: $$\{ -2,\ 5,\ 7 \}$$
- **Range**: $$\{ 4,\ 5,\ 13 \}$$
- **Is it a function?**: **No**, because the input $$5$$ corresponds to multiple outputs.
- **Domain**: $$\{ -2,\ 5,\ 7 \}$$ - **Range**: $$\{ 4,\ 5,\ 13 \}$$ - **Function**: No, because the input $$5$$ has two different outputs.

Functions
State the domain and range for the following relation. Then determine whether the relation represents a function.

Part 1 of 3

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Functions State the domain and range for the following relation. Then determine whether the relation represents a function. Part 1 of 3