Math Problem Statement

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

Solution

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

Let's examine each option:

  1. Option F: {(4,17),(2,6),(1,3),(1,10)}\{(4, \sqrt{17}), (2, \sqrt{6}), (1, \sqrt{3}), (1, \sqrt{10})\}

    • Here, the xx-value 11 appears twice, associated with two different yy-values (3\sqrt{3} and 10\sqrt{10}).
    • This does not satisfy the requirement for a function since an xx-value should not map to more than one yy-value.
    • Therefore, F is not a function.
  2. Option G: {(7,2.9),(15,5.9),(15,8.9),(7,11.9)}\{(-7, 2.9), (-15, 5.9), (-15, 8.9), (-7, 11.9)\}

    • Here, both 7-7 and 15-15 each appear twice as xx-values, each with different yy-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)}\{(11.1, 7), (5.1, 4), (12.1, 5), (6.1, 7)\}

    • Each xx-value here is unique, meaning no xx-value is repeated.
    • This satisfies the requirement for yy to be a function of xx.
    • Therefore, H is a function.
  4. Option J: {(1,3),(2,4),(1,5),(6,7)}\{(\sqrt{1}, -3), (\sqrt{2}, -4), (\sqrt{1}, -5), (\sqrt{6}, -7)\}

    • The xx-value 1\sqrt{1} (which is 1) appears twice, each time with a different yy-value (3-3 and 5-5).
    • 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)

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Math Problem Analysis

Mathematical Concepts

Functions
Ordered Pairs
Mapping Relations

Formulas

-

Theorems

Definition of a Function

Suitable Grade Level

Grades 9-10