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1.7 All Transformations

This document discusses sketching graphs of functions by applying transformations to parent functions. The key points are: 1. Graphs can be derived from parent functions by applying transformations in sequential order, from left to right. 2. The general form of a transformed function is y = af(k(x - d)) + c, where a stretches vertically, k stretches horizontally, d translates horizontally, and c translates vertically. 3. Examples are provided to demonstrate describing transformations from equations and writing equations from descriptions of transformations.

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Ashley Elliott
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588 views3 pages

1.7 All Transformations

This document discusses sketching graphs of functions by applying transformations to parent functions. The key points are: 1. Graphs can be derived from parent functions by applying transformations in sequential order, from left to right. 2. The general form of a transformed function is y = af(k(x - d)) + c, where a stretches vertically, k stretches horizontally, d translates horizontally, and c translates vertically. 3. Examples are provided to demonstrate describing transformations from equations and writing equations from descriptions of transformations.

Uploaded by

Ashley Elliott
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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MHF4U Unit 1 Lesson 7 1

1.4  Sketching  Graphs  of  Functions    


Learning  Goal  
 
•   To  apply  transformations  to  parent  functions:  𝒚 = 𝒂𝒇%𝒌(𝒙 − 𝒅), +  𝒄          
•   To  be  able  to  describe  each  transformation  when  given  a  function  using  the  correct  
terminology  –  vertical/horizontal  stretch/compressions,  vertical/horizontal  translations  and  
reflections  
•   To  be  able  to  determine  an  equation  when  given  the  transformations  in  a  statement  
 
 
Order  of  Transformations  
 
Graphs  of  functions  can  be  derived  from  their  parent  functions  by  applying  transformations  in  
sequential  order.      
The  general  form  of  a  transformed  function  is  
 
𝒚 = 𝒂𝒇(𝒌(𝒙 − 𝒅) +  𝒄  
 
Translations  are  applied  in  the  order  from  left  to  right  and  can  be  described  as:  
 
1.      
 
 
     
2.  
 
 
 
3.  
 
 
 
4.  
 
 
 
5.  
 
 
6.  
 
 
 
 
 
 
MHF4U Unit 1 Lesson 7 2
Example    –  State  the  transformations  defined  by  each  equation  given  below:  
 
 
 
𝟏     5𝒙6𝟐
a)  𝒚 =    𝒇(𝒙 − 𝟑) + 𝟕              
𝟒  
    b)    𝒚 =   −𝒇 4 9   𝟓
 
 
 
 
 
 
 
 
 
Example    –  the  point  (8,2)  is  on  the  graph  of  y  =  f(x).    Determine  the  corresponding  coordinates  of  
this  point  on  the  graph  of  𝒚 =   −𝟐  𝒇%𝟐(𝒙 + 𝟏), −  𝟒  
 
 
 
 
 
 
 
 
 
 
 
 
Example    -­‐  State  the  name  and  equations  of  the  parent  function.    Describe  the  given  transformation  in  
words.    State  the  domain  and  range  of  each  function.  
 
?
a)    𝑓(𝑥 ) =     (𝑥 − 3)= + 7                                                          b)    𝑓(𝑥 ) =     A2(𝑥 + 5)   − 4  
@
 
 
 
 
 
 
 
 
 
 
 
 
MHF4U Unit 1 Lesson 7 3
5G
c)    𝑓(𝑥 ) =   −6(25F ) −  3                                                          d)    𝑓 (𝑥 ) = =(F6?) + 8  
 
 
 
 
 
 
 
 
 

?
Example  –  Given:    𝑓 (𝑥 ) =   F      The  graph  of  the  given  function  is  transformed  as  stated  below.    Write  

the  equation  of  the  new  function.  

a)   Reflection  across  the  x-­‐axis,  horizontal  stretch  by  a  factor  of  2,  up  7  units.  

? ?
b)   vertical  compression  by  a  factor  of  I,  horizontal  compression  by  a  factor  of  J,  left  3  units  and  
down  6  units  
 
 
 
 
 
Example-­‐  Given  𝑔(𝑥 ) = √𝑥    Express  the  given  functions  using  g(x)  notation.  
 
?
a)      𝑦 =   √𝑥 − 2                                        b)    𝑦 =   √𝑥 + 1                                        c)    𝑦 =   O  A– (𝑥 + 1) − 2  

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