IB DP Maths: AA HL复习笔记2.5.1 Reciprocal & Rational Functions
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?
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This is the value that causes the denominator to be zero
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- 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
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?
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Where p, q, r are constants- This can be done by polynomial division or comparing coefficients
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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
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