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IB DP Maths: AA SL復(fù)習(xí)筆記2.5.3 Stretches of Graphs

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月15日 下午6:37

Stretches of Graphs

What are stretches of graphs?

  • When you alter a function in certain ways, the effects on the graph of the function can be described by?geometrical transformations
  • For a?stretch:
    • the graph is?stretched?about one of the coordinate axes by a scale factor
      • Its size?changes
    • the orientation of the graph remains?unchanged
  • A particular stretch is specified by a?coordinate axis?and a?scale factor:
    • The?distance?between a?point?on the graph and the?specified coordinate axis?is?multiplied?by the?constant scale factor
    • The graph is stretched in the?direction?which is?parallel?to the?other coordinate axis
    • For scale factors?bigger than 1
      • the points on the graph get?further away?from the?specified coordinate axis
    • For scale factors?between 0 and 1
      • the points on the graph get?closer?to the?specified coordinate axis
      • This is also called a?compression

2.9.2-Stretches-What-Is

What effects do horizontal stretches have on the graphs and functions?

2.9.2-Stretches-statement_horiz_Illustration

 

What effects do vertical stretches have on the graphs and functions?

2.9.2-Stretches-statement_vert_Illustration

Exam Tip

  • To get full marks in an exam make sure you use correct mathematical terminology
    • For example: Stretch vertically by scale factor ?
    • Do not use the word "compress" in your exam

Worked Example

2-5-3-ib-aa-sl-stretch-graph-a-we-solution

2-5-3-ib-aa-sl-stretch-graph-b-we-solution

 

 

 

 

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