Name:____________________________
Maus/Calculus
Date:_______
End Behavior
POD:
Graph the following functions on your calculator:
( )
( )
( )
( )
Compare these graphs. What do you notice about them in terms of similarities and
differences?
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What happens to these graphs as
?
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What happens to these graphs as
?
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Without graphing, what happens to the graph of ( )
as
and as
?
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Without graphing, what happens to the graph of ( )
as
and as
?
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Write a generalization about functions with even exponents
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1
Part 2
Graph the following functions on your calculator:
( )
( )
( )
( )
Compare these graphs. What do you notice about them in terms of similarities and
differences?
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
What happens to these graphs as
?
_____________________________________________________________________
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What happens to these graphs as
?
_____________________________________________________________________
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Without graphing, what happens to the graph of ( )
as
and as
?
_____________________________________________________________________
_____________________________________________________________________
Without graphing, what happens to the graph of ( )
as
and as
?
_____________________________________________________________________
_____________________________________________________________________
Write a generalization about functions with odd exponents
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_____________________________________________________________________
_____________________________________________________________________
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2
Part 3
Graph the following functions on your calculator:
( )
( )
( )
Compare these graphs. What do you notice about them in terms of similarities and
differences?
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
What happens to these graphs as
?
_____________________________________________________________________
_____________________________________________________________________
What happens to these graphs as
?
_____________________________________________________________________
_____________________________________________________________________
Without graphing, what happens to the graph of ( )
as
and as
?
_____________________________________________________________________
_____________________________________________________________________
Without graphing, what happens to the graph of ( )
as
and as
?
_____________________________________________________________________
_____________________________________________________________________
Write a generalization about functions with fractional even exponents
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_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
3
Part 4
Graph the following functions on your calculator:
( )
( )
( )
Compare these graphs. What do you notice about them in terms of similarities and
differences?
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
What happens to these graphs as
?
_____________________________________________________________________
_____________________________________________________________________
What happens to these graphs as
?
_____________________________________________________________________
_____________________________________________________________________
Without graphing, what happens to the graph of ( )
as
and as
?
_____________________________________________________________________
_____________________________________________________________________
Without graphing, what happens to the graph of ( )
as
and as
?
_____________________________________________________________________
_____________________________________________________________________
Write a generalization about functions with fractional odd exponents
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
4
Part 5 (Very Important)
What is the value of any number, c, divided by infinity?
Look at
as
Look at
as
Look at
as
Look at
as
. What happens?
. What happens?
. What happens?
. What happens?
This leads to a convenient trick when finding limits as
Find the limit of each function:
5
or as
.
Find the limit of each function.
6