**Unformatted text preview: **Review hard
Transforming The graph of a natural exponential function
Question
Below is he graph of yz ex
Transform? IT To make negraph of yo -extz
given The range and domain of ye - ext?
using
Interval notation .
Explanation
Background: Here are Some ways To Transform The graph
of a function . .
1. Translate he graph horizontaly
eig . y = f ( x - C ) we shift ne graph of y = f (x ) To re rightcom
2. Reflect ne graph across an acis
ergy = - f (c) , we reflect me graph of y = f ( xc ) a cross re
2 akis y = f ( xx ), we reflect me graph of y= fled across my-axis .
3 , Translate he graph verticaly
e . g , y = f Gil t c , we shift The graph of yef (y upward
Nofe is is a good idea To perform The Transformations in Te
above order.
The current problem:
yse we are given the graph yzer is has a horizontal
asyn tore y- The range is ( 0, 0) re domain ( = 00100)
- 4= e2+ 2
we'll use me graph of y= e To graph y=eat ?
So we Translate y= ex To me left 2 units The horizontal
asymptote is srill yes the range and domain are pe and
- yE - e To do This, we reflect he graph of yee?tz
across ne -axis . The range "is now (-00, 0), and me
domain is saill (- 0s, 09)
If moving upward of downward Mostzonfal wynyfore
becomes Map, eng upwad 6 units from o ha is y= 6...

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- Fall '06
- Moffett
- Derivative, Complex number, ergy, Mostzonfal wynyfore