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IB DP Maths: AA HL复习笔记2.5.1 Reciprocal & Rational Functions
Category:
IB课程
,
教材笔记
,
福利干货
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
d
oes 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
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
转载自savemyexams
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