q   Pick  up  U3L2  from  the  side  shelf  à  à  à q   Tonight’s  HW:

o HW  #3  –  Pg.  143  #13-­‐33  odd  (SKIP  #25  and  #31)

q   Updates: o Unit  3  Quiz  1  (3.1-­‐3.3) 3rd/5th    will  be  10/9              

Welcome  Pre-­‐Calc!

① Return  Work ② New  HW  Late  Passes  

③ Finish  U3L1 ④ U3L2

⑤ Cool-­‐Down…

Students  who  need  to  take  Assessments:   Ø  Please  take  them  before  break!

Agenda

I  am  returning  all  work  that  I  have  of  yours. o  The  Unit  1  Projects  will  be  handed  back  the  Monday  we  get  back  from  break.

o  Unit  2  Assessment  will  be  returned  the  Monday  we  get  back  from  break.

Returning  Work

As  promised,  every  6  weeks  you  will  earn  one  HW  late  pass.   I  will  collect  these  the  day  before  Progress  Report  2.  

New  HW  Late  Passes  

What  are  your  questions?

Gather  all  homework's  in  one  pile  and  place  them  in  the  middle  of  your  tables.  I  will  come  around  and  pick  them  

up.  

Review  HW#2  –  Pg.  135  #15-­‐27  odd

① Classify  functions  as  even  or  odd.

② Use  transformations  to  graph  a  function  by  moving  or  resizing  a  parent  function.  

 

Learning  Objectives  

Common  names  you  heard  with  symmetry  in  Algebra  2  were  even  and  odd. o  In  your  tables,  discuss  what  you  remember  about  even  and  odd  functions.  

3.1  Symmetry  and  Coordinate  Graphs

Even  Functions o  Symmetric  with  respect  to  the  y-­‐axis. o  f(-­‐x)  =  f(x)

Odd  Functions o  Symmetric  with  respect  to  the  origin.   o  f(-­‐x)  =  -­‐f(x)  

   

3.1  Symmetry  and  Coordinate  Graphs

Go  back  to  practice  (2)  and  determine  algebraically  which  is  even,  odd,  or  neither.    

   

3.1  Symmetry  and  Coordinate  Graphs

Pair-­‐Share  -­‐  Seat  #1  and  Seat  #2  /  Seat  #3  and  Seat  #4   o  Discuss  what  you  remember  from  your  previous  courses  about  transformations.

o  Discuss  what  you  remember  about  parent  functions.  Name  as  many  parent  functions  as  you  can.  

Brainstorm!  

Real  life  activities  can  be  modeled  using  graphs.  

3.2  Families  of  Graphs

Parent  Graph o  A  basic  graph  that  is  transformed  to  create  other  members  in  a  family  of  graphs.  

Ø With  your  arms  show  me  a  constant  function.   Constant  Function o  f(x)  =  c   where  c  is  a  constant.    

3.2  Families  of  Graphs

Identity  Function o  f(x)  =  x   o  Also  known  as  a  Linear  Function.     o Main  Piece(s):  slope  of  1  and  goes  through  origin.   Polynomial  Function o  f(x)  =  x2 o  Also  known  as  Quadratic  Function. o Main  Piece(s):  Vertex  at  the  origin

3.2  Families  of  Graphs

Polynomial  Function o  f(x)  =  x3 o  Also  known  as  Cubic  Function.   o Main  Piece(s):  Goes  through  the  origin.   Square  Root  Function o  f(x)  =  √x o Main  Piece(s):  Starts  at  the  origin.      

3.2  Families  of  Graphs

Absolute  Value  Function o  f(x)  =  |x| o Main  Piece(s):  Vertex  at  the  origin  and  has  a  slope  of  1  and  -­‐1.

Rational  Function o  f(x)  =  1/x                  OR o  f(x)  =  x  -­‐1 o Main  Piece(s):  Use  origin  as  the  center                  BUT  our  graph  does  not  include  the  origin.

3.2  Families  of  Graphs

As  a  connection  to  our  lesson  on  Monday,  discuss  in  your  groups  the  type  of  symmetry  the  parent  functions  demonstrate.

3.2  Families  of  Graphs

Transformations o Moving  and/or  resizing  parent  graphs.   o  Types  of  Transformations  include:  replections,  translations,  and  dilations.

You  are  going  to  be  completing  an  exploration  on  transformations  in  your  groups,  but  before  I  set  you  off  lets  set  your  paper  up  for  perfection!

3.2  Families  of  Graphs

The  parent  function  we  are  going  to  choose  is  square  root.  Since  we  are  choosing  square  root  I  am  going  to  pill  in   Parent  Function:  f(x)  =  ___   on  guided  notes.   I  am  going  to  demonstrate  the  type  of  work  I  expect  from  you  all  on  the  whiteboard  for  replection.  

3.2  Families  of  Graphs

         

Type%of%Transformation%Parent%Function:%!(!) !=%_______%%

1.%Fill%in%the%y%=%with%the%transformed%equation.%2.%Graph%the%parent%in%one%color%using%the%graphing%calculator%(be%precise).%%3.%Graph%the%transformed%function(s)%in%a%different%color.%4.%Describe%how%the%transformed%function%changed%the%parent.%

Reflection%! = −!(!)!!Is!reflected!over!the!______________.!%%%%%%

%! =!0!________!

!

3.2  Families  of  Graphs

       

3.2  Families  of  Graphs

       

3.2  Families  of  Graphs

       

3.2  Families  of  Graphs

Transformations  Continued…   o  Inside  Opposite,  Outside  Same.   o  Inside  the  function  is  horizontal  change,  outside  is  vertical  change.  

 

3.2  Families  of  Graphs

Identify  the  parent  function.  Then  graph  the  transformed  function  on  your  whiteboards.   (1) Y  =  (x  +  3)2

(2) Y  =  |x|  -­‐  2

(3) Y  =  3x3

Whiteboards!

Performing  More  than  One  Transformation o Work  from  the  inside  to  the  outside.  Similar  to  how  you  would  use  the  order  of  operations  (PEMDAS).  

 

3.2  Families  of  Graphs

Identify  the  parent  function.  Then  graph  the  transformed  function  on  your  whiteboards.  

Whiteboards!

TIP:  When  graphing  transformed  functions  I  usually  color  code  my  work  (just  like  everything  I  do).  I  graph  my  parent  in  one  color.  Show  all  my  transformations  in  pencil  and  graph  my  pinal  transformed  function  in  a  different  colored  pen.  Use  your  graphing  calculator  to  check  your  work! (1)$Practice:$Identify$the$parent$function.$Graph$each$function.$Describe$the$transformation(s)$from$the$parent$function.$$(a)$! = − ! − 3+ 2$ (b)$! = !

!!!$+$1$$$$$$$$$$

$

3.2  Families  of  Graphs

I  am  going  to  place  a  transformed  function  on  the  PowerPoint  and  you  are  going  to  model  the  transformed  function  using  your  body.   If  it  is  horizontal  translation  slide  left  or  right. If  vertical  translation  step  up  or  down. If  dilation  open  your  arm(s)  more  or  less  for  stretch/compression. If  replection  demonstrate  with  your  arms.  

Cool-­‐Down:  Function  Workout!

f(x)=2+√x  

Cool-­‐Down:  Function  Workout!

f(x)=(-­‐x)3-­‐3  

Cool-­‐Down:  Function  Workout!

f(x)=(x-­‐1)2+1  

Cool-­‐Down:  Function  Workout!

f(x)=2|x|-­‐1  

Cool-­‐Down:  Function  Workout!

f(x)=|-­‐x|  

Cool-­‐Down:  Function  Workout!

Pick  one  transformation  and  write  that  one  transformation  on  a  whiteboard.   Describe  how  to  identify  it  in  an  equation  to  your  tablemates.  

Cool-­‐Down