Lesson_5.1_Graphing_Reciprocal_Functions.notebook
1
October 21, 2009
5.1 Graphing Reciprocal Functions
Unit 5:
Rational Functions, Equations and Inequalities
Recall:
•
The parent reciprocal F
cn
:
f(x) = 1/x
•
f(x) is the reciprocal of
g(x) = x
.
•
So... in actual fact
f(x)
and
g(x)
are called
a pair of reciprocal functions b/c
f(x) = 1/g(x)
Investigation:
in your notes graph each set
Function 
g(x)
Reciprocal 
f(x)
Graph
Asymptotes
g(x) = x3
g(x) = x
2
4
g(x) = 1x
2
g(x) = (x+1)
2
4
f(x) =
1
x3
f(x) =
1
x
2
4
f(x) =
1
1x
2
f(x)=
1
(x+1)
2
4
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Lesson_5.1_Graphing_Reciprocal_Functions.notebook
2
October 21, 2009
Investigation cont...
Compare the graph of
f(x)
and
g(x)
and answer:
1. How are the intervals of increase / decrease of
f(x)
and
g(x)
related?
2. What are the X values for f >0 vs.
g>0?
3. What are the X values for f<0
vs. g<0 ?
4. Where do f and g intersect?
What do all those P.O.Is have in common?
Reciprocal Functions: Summary
(1)
The zeroes of the original function become the vertical
asymptotes on the reciprocal function.
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 Spring '11
 sda
 Equations, Critical Point, Inequalities, Rational Functions, Optimization, Fermat's theorem, reciprocal function

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