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3.1 – When One Thing Depends on Another


  • Describe relationships of dependence for real-world functional relationships.
  • Identify functional relationships in nature.


Key Terms

  • Function – A special type of relationship in algebra where two quantities are related to each other so that one quantity depends on (or is a function of) the other.



  • (x,y) represents a point on a coordinate plane
    • x: Domain (Independent Variable)
    • y: Range (Dependent Variable)


  • What is a Function?
    • One quantity depends on another
    • As one quantity changes, the other quantity changes
    • Depends on = Is a Function of
      • y depends on x
      • y is a function of x


Example: Tree Height vs Years of Growth

  • In English: The height of the tree depends on the years it has been growing.
  • In algebra: The height of the tree is a function of the years it has been growing.
  • Facts
    • x: years the tree has been growing (independent)
    • y: height of the tree (dependent)


Example: Radius of Table vs Paint

  • The larger the radius of the surface of a circular table, the more paint you will need to cover the surface.
  • The amount of paint needed is a function of the radius.
  • Facts
    • x: radius of the table (independent)
    • y: amount of paint (dependent)


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