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IB DP Maths: AA HL復習筆記2.5.1 Reciprocal & Rational Functions

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月12日 上午10:38

What is the reciprocal function?

What are the key features of the reciprocal graph?

  • The graph?does not have a?y-intercept
  • The graph?does not have any roots
  • The graph has?two asymptotes

  • The graph?does not have any minimum or maximum points

Linear Rational Functions & Graphs

What is a rational function with linear terms?

  • The?reciprocal function?is a?special case?of a rational function

What are the key features of linear rational graphs?

      • This is the value that causes the denominator to be zero
  • The graph?does not have any minimum or maximum points
  • If you are asked to?sketch or draw?a rational graph:
    • Give the?coordinates?of any?intercepts?with the axes
    • Give the?equations?of the?asymptotes

Exam Tip

  • If you draw a horizontal line anywhere it should only intersect this type of graph once at most
  • The only horizontal line that should not intersect the graph is the horizontal asymptote
    • This can be used to check your sketch in an exam

Worked Example

2-4-1-ib-aa-sl-rational-func-a-we-solution

2-4-1-ib-aa-sl-rational-func-b-we-solution

2-4-1-ib-aa-sl-rational-func-c-we-solution

 

Quadratic Rational Functions & Graphs

How do I sketch the graph of a rational function where the terms are not linear?

What are the key features of rational graphs: quadratic over linear?

      • Where p, q, r?are constants
      • This can be done by?polynomial division?or?comparing coefficients

What are the key features of rational graphs: linear over quadratic?

Exam Tip

  • If you draw a horizontal line anywhere it should only intersect this type of graph twice at most
    • This idea can be used to check your graph or help you sketch it

Worked Example

2-5-1-ib-aa-hl-quad-rational-function-a-we-solution

2-5-1-ib-aa-hl-quad-rational-function-b-we-solution

2-5-1-ib-aa-hl-quad-rational-function-c-we-solution
轉載自savemyexams

以上就是關于【IB DP Maths: AA HL復習筆記2.5.1 Reciprocal & Rational Functions】的解答，如需了解學校/賽事/課程動態，可至翰林教育官網獲取更多信息。

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