Determine whether the relation is a function. Give the domain and the range of the relation.
​{(5​,4​),(5​,7​),(7​,4​),(7​,7​)}
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Part 1
Is this a​ function?

A relation is considered a **function** if each input (the first element in each ordered pair) is associated with exactly one output (the second element in the pair). 

Given the relation:
\[
\{(5, 4), (5, 7), (7, 4), (7, 7)\}
\]
we can observe that:

- The input 5 is associated with both 4 and 7.
- The input 7 is also associated with both 4 and 7.

Since the input 5 corresponds to two different outputs (4 and 7), this relation **is not a function**.

### Domain and Range:
- **Domain**: The set of all inputs (first elements): \(\{5, 7\}\)
- **Range**: The set of all outputs (second elements): \(\{4, 7\}\)

### Summary:
- **Is it a function?** No.
- **Domain**: \(\{5, 7\}\)
- **Range**: \(\{4, 7\}\)

Would you like further clarification or details on this concept?

Here are five related questions to expand on this information:
1. What are the key differences between a function and a relation?
2. How can you graphically determine if a relation is a function?
3. Can a function have the same output for different inputs?
4. What is the vertical line test for functions?
5. What are some examples of real-world functions?

**Tip**: When checking if a relation is a function, remember that each input must map to exactly one output!

Determine whether the relation is a function. Give the domain and the range of the relation. {(5,4),(5,7),(7,4),(7,7)}

Learn how to determine if a relation is a function using the example {(5,4), (5,7), (7,4), (7,7)}. Understand key concepts such as the definition of a function, domain, and range, with step-by-step explanations. Suitable for students in Grades 9-11.

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