https://file.aiquickdraw.com/mathbot/file/1726015874322ksnl3fh6.jpg

To determine which relation is also a function, we must review the definition of a function. A relation is a function if, for every input (first element of each ordered pair), there is exactly one output (second element of the ordered pair). In other words, no two pairs should have the same first element with different second elements.

Let's analyze the relations provided in the image:

1. **Relation 1: {(0, 3), (1, 2), (1, 4), (2, 1)}**
   - Here, the first element "1" appears twice: (1, 2) and (1, 4), which means that "1" maps to two different outputs (2 and 4). Hence, this is *not* a function.

2. **Relation 2: {(-4, 5), (0, -3), (1, 3), (4, -3)}**
   - All first elements are unique: -4, 0, 1, and 4. Since no input is repeated, this *is* a function.

3. **Relation 3: {(2, 4), (2, -2), (2, 1), (2, 3)}**
   - The first element "2" appears multiple times with different outputs (4, -2, 1, and 3). Therefore, this is *not* a function.

4. **Relation 4: {(-1, 3), (0, 2), (3, -1), (3, 2)}**
   - The first element "3" appears twice: (3, -1) and (3, 2), meaning "3" maps to two different outputs (-1 and 2). Hence, this is *not* a function.

### Conclusion:
The relation that is also a function is **Relation 2: {(-4, 5), (0, -3), (1, 3), (4, -3)}**.

Would you like a further explanation of functions or the steps involved? 

Here are 5 related questions:
1. What is the difference between a function and a relation?
2. How do you determine if a graph represents a function?
3. What is the vertical line test for functions?
4. Can a function have the same output for different inputs?
5. What are examples of real-world situations that can be modeled as functions?

**Tip:** Always check if any input (x-value) is repeated with different outputs (y-values) when determining if a relation is a function.

Which relation is also a function? (Options provided in the image)

Learn how to identify which relation is a function by checking if each input maps to a single output. This algebra problem involves analyzing sets of ordered pairs, perfect for students in Grades 7-9.

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