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To determine which set of ordered pairs represents \( y \) as a function of \( x \), we need to verify that for each input \( x \), there is only one corresponding \( y \) value. In other words, \( y \) is a function of \( x \) if each \( x \)-value in the set of ordered pairs is unique.

Let's examine each option:

1. **Option F**: \(\{(4, \sqrt{17}), (2, \sqrt{6}), (1, \sqrt{3}), (1, \sqrt{10})\}\)
   - Here, the \( x \)-value \( 1 \) appears twice, associated with two different \( y \)-values (\( \sqrt{3} \) and \( \sqrt{10} \)).
   - This does not satisfy the requirement for a function since an \( x \)-value should not map to more than one \( y \)-value.
   - Therefore, **F is not a function**.

2. **Option G**: \(\{(-7, 2.9), (-15, 5.9), (-15, 8.9), (-7, 11.9)\}\)
   - Here, both \( -7 \) and \( -15 \) each appear twice as \( x \)-values, each with different \( y \)-values.
   - This also does not satisfy the requirement for a function.
   - Therefore, **G is not a function**.

3. **Option H**: \(\{(11.1, 7), (5.1, 4), (12.1, 5), (6.1, 7)\}\)
   - Each \( x \)-value here is unique, meaning no \( x \)-value is repeated.
   - This satisfies the requirement for \( y \) to be a function of \( x \).
   - Therefore, **H is a function**.

4. **Option J**: \(\{(\sqrt{1}, -3), (\sqrt{2}, -4), (\sqrt{1}, -5), (\sqrt{6}, -7)\}\)
   - The \( x \)-value \( \sqrt{1} \) (which is 1) appears twice, each time with a different \( y \)-value (\( -3 \) and \( -5 \)).
   - This does not satisfy the requirement for a function.
   - Therefore, **J is not a function**.

Based on this analysis, the correct answer is:

**Option C (H)**

Which set of ordered pairs represents y as a function of x?

Understand how to determine if a set of ordered pairs represents a function by analyzing unique mappings between x and y values. This problem explores key concepts in functions and is suitable for students in Grades 9-10.

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