https://file.aiquickdraw.com/mathbot/file/1726901415329bm1djemy.jpg

The statement in the image says:

"A function is one-to-one if the set of ordered pairs are unique and distinct, that is there should be no repetition of \( x \) and \( y \) values."

This statement is **False**.

### Explanation:
For a function to be one-to-one (or injective), each unique \( x \)-value must map to a unique \( y \)-value, meaning no two different \( x \)-values should map to the same \( y \)-value. However, the statement incorrectly suggests that there should be no repetition of both \( x \) and \( y \) values.

- **Correct condition for one-to-one function**: No two distinct \( x \)-values have the same \( y \)-value.
- **Incorrect condition**: No repetition of \( x \) and \( y \) values implies that both the domain and the range should be unique, which is not necessary for a function to be one-to-one.

Would you like more details or have any questions? Here are five related questions:

1. What is the definition of a bijective function?
2. How do you determine if a function is one-to-one using a graph?
3. Can a function be one-to-one but not onto? Explain.
4. What is the horizontal line test and how is it used?
5. How

A function is one-to-one if the set of ordered pairs are unique and distinct, that is there should be no repetition of x and y values.

Explore the concept of one-to-one functions (injective) and understand why the condition of no repetition of x and y values is incorrect. Suitable for students in Grades 9-12.

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