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The given function is \( f(x) = |x| \), which represents the absolute value of \( x \).

A function is **one-to-one** (or injective) if every element in the domain maps to a unique element in the range. This means that if \( f(x_1) = f(x_2) \), then \( x_1 = x_2 \).

For \( f(x) = |x| \):
- \( f(x) = f(-x) \), for example, \( f(2) = 2 \) and \( f(-2) = 2 \).
- This means that the same output (like 2) can come from different inputs (like 2 and -2).

Thus, \( f(x) = |x| \) is **not** one-to-one, because multiple inputs (both positive and negative) can produce the same output.

The correct answer to enter is:
- **"n"**

Would you like more details on one-to-one functions or have any questions? 

Here are some related questions for further practice:
1. Is the function \( f(x) = x^2 \) one-to-one? Why or why not?
2. How would you determine if a piecewise function is one-to-one?
3. What is the difference between injective and surjective functions?
4. Can a function be both one-to-one and onto? Give an example.
5. How does the horizontal line test help in determining if a function is one-to-one?

**Tip:** For a function to be one-to-one, its graph should pass the horizontal line test — no horizontal line should intersect the graph more than once.

A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. If it is one-to-one, enter 'y' below. If not, enter 'n' below. f(x) = |x|

This problem explores whether the absolute value function f(x) = |x| is one-to-one. Learn how to apply the horizontal line test and the definition of injective functions. Suitable for high school students in Grades 9-11.

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