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Fill in the blanks below in order to justify whether or not the mapping shown represents a function.

Set ASet B75-4-108-3

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Attempt 1 out of 2

The mapping diagram above  does NOT representrepresents a function since  there is one numberfor each number in  Set A (the input)Set A (the output)Set B (the output)Set B (the input) where there  are multiple mappingsis no mappingis only one mapping  to Set B (the input)from Set A (the output)to Set B (the output)from Set A (the input).

To justify whether the mapping represents a function, we need to consider the definition of a function. A function is a relation where each input (from Set A) is mapped to exactly one output (in Set B). In other words, for each element in Set A, there can be only one corresponding element in Set B.

Let's fill in the blanks step by step:

**Answer:**

The mapping diagram above **does NOT represent** a function since **there is one number in Set A (the input)** where **there are multiple mappings** to **Set B (the output)**.

### Explanation:

1. **A function**: A relation is a function if every input has exactly one output.
2. **In this case**: There is an input in Set A (the input) that has more than one corresponding output in Set B, which violates the definition of a function.
3. **Multiple mappings**: This is why the mapping does not represent a function, as one input can only correspond to one output in a function.

Would you like further details or clarifications on this? Here are five questions to explore the topic further:

1. What is the difference between a relation and a function in mathematics?
2. How can you visually identify a function using a mapping diagram?
3. What happens if two different inputs are mapped to the same output?
4. Can an input in Set A map to no elements in Set B? Would that still be a function?
5. How does the vertical line test apply to determining if a graph represents a function?

### Tip:
When determining if a mapping represents a function, always check if every element in the input set (domain) maps to exactly one element in the output set (codomain).

Fill in the blanks below in order to justify whether or not the mapping shown represents a function. Set ASet B75-4-108-3

Understand how to justify whether a mapping represents a function. This problem explains the definition of a function and how to check if every element in the input set has exactly one corresponding output. Suitable for students in Grades 6-8.

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