- Describe relationships of dependence for real-world functional relationships.
- Identify functional relationships in nature.
- 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.
- 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.
- x: radius of the table (independent)
- y: amount of paint (dependent)