Functional Dependency Math Example 1

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

Example 1

easy
Is yy functionally dependent on xx in the equation y=3x+1y = 3x + 1?

Solution

  1. 1
    Step 1: For any xx, there is exactly one y=3x+1y = 3x + 1.
  2. 2
    Step 2: x=0→y=1x = 0 \to y = 1, x=1→y=4x = 1 \to y = 4. Each input gives one output.
  3. 3
    Step 3: Yes, yy is a function of xx.

Answer

Yes, yy depends functionally on xx.
Functional dependency means each input determines exactly one output. The equation y=3x+1y = 3x + 1 passes the vertical line test — every xx maps to a unique yy.

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 2 medium

Is [formula] functionally dependent on [formula] in [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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