# 3.1 – When One Thing Depends on Another

Objectives

• 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.

Notes

• (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)