Functions and Relations

• Is this a relation?

  Determining the domain and range from input and output values
• Which relation mapping represents a function?

  Identifying the correct mapping that represents a function
• Definitions

  • A relation between two variables x and y is a set of ordered pairs
  • An ordered pair consists of an x and y-coordinate
  • A relation may be viewed as ordered pairs, mapping design, table, equation, or written in sentences
  • x-values are input, independent variable, domain
  • y-values are output, dependent variable, range
• Is a relation a function?

  • A function pairs each domain value with exactly one range value
  • Focus on the x-coordinates to determine if it is a function
  • Different x-coordinates indicate a function, same x-coordinates indicate not a function
  • Y-coordinates do not affect the determination of functions
• What makes this a relation?

  Determining the domain and range from a set of ordered pairs
• Vertical Line Test


  A relation is a function if a vertical line drawn through its graph passes through only one point