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3.6 – Functions and Graphs

Objectives

  • Identify ordered pairs in a mapping diagram.
  • Identify domain and range using ordered pairs.
  • Graphically define the domain and range of a function.
  • Use the vertical line test to determine whether a graph is a function.
  • Relate a graph to the function it models.

 

Key Terms

  • Ordered Pair – A pair of numbers in parentheses that names the location of a point on a coordinate plane.
    • (x,y) is always in alphabetical order.
      • Example: (4,-3)
      • Graph this point by starting at the origin (0,0), go to the right (x-value) by 4, then go down (y-value) by 3.
  • Vertical – Straight up and down.
    • On a coordinate plane, the equation of a vertical line is x=a, where a is a constant.
  • Horizontal – Straight left and right.
    • On a coordinate plane, the equation of a horizontal line is y=a, where a is a constant.
  • Vertical Line Test – A method for testing whether a given graph is a function.
    • If a vertical line intersects the graph at 2 or more points, it is NOT a function.
    • If a vertical line intersects the graph at only 1 point, it IS a function.

Alg1A 3.06 Function Ex

 

Notes

Alg1A 3.06 Rules


  • Example: Is this a function?  Also, find the Domain & Range
    • Step 1: Draw a vertical line.  Do you cross the graph once or more than once?
      • You cross the graph once, so this IS a function
    • Step 2: Domain (all the x-values)
      • How far LEFT does your graph go?  Answer: 0
      • How far RIGHT does your graph go?  Answer: Infinity
        • So, x \geq 0
    • Step 3: Range (all the y-values)
      • How far UP does your graph go?  Answer: Infinity
      • How far DOWN does your graph go?  Answer: 0
        • So, y \geq 0

 

Alg1A 3.06 Graph01

 

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