Functional Dependency Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Is yy functionally dependent on xx in x2+y2=25x^2 + y^2 = 25?

Solution

  1. 1
    Step 1: Solve for yy: y=±25−x2y = \pm\sqrt{25 - x^2}.
  2. 2
    Step 2: For x=3x = 3: y=±4y = \pm 4. Two outputs for one input!
  3. 3
    Step 3: No, yy is not a function of xx (fails the vertical line test).

Answer

No, yy is not uniquely determined by xx.
A circle is not a function because each xx (except at the endpoints) gives two yy values. You'd need to restrict to the upper or lower semicircle to get a function.

About Functional Dependency

A relationship where the value of one quantity (the output or dependent variable) is completely determined by the value of another quantity (the input or independent variable). If yy depends on xx, then knowing xx uniquely determines yy.

Learn more about Functional Dependency →

More Functional Dependency Examples

Example 1 easy

Is [formula] functionally dependent on [formula] in the equation [formula]?

Example 3 easy

Does [formula] represent a function?

Example 4 medium

In a class, is final grade a function of student name?

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