Pass out student note handouts

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• Pass out student note handouts

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On graph paper, graph the following functions
1.7 Transformations of Functions
https//www.desmos.com/calculator
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• I. There are 4 basic transformations for a
  function f(x).
• y A f (Bx C) D
• A) f(x) D (moves the graph ? and
  ?)
• B) A f(x)
• 1) If A gt 1 then it is vertically
  stretched.
• 2) If 0 lt A lt 1, then its a vertical
  shrink.
• 3) If A is negative, then it flips over the
  x-axis.
• C) f(x C) (moves the graph ? and ?)
• D) f(Bx) or f(B(x)) (factor out the B term if
  possible)
• 1) If B gt 1 then its a horizontal shrink.
• 2) If 0 lt B lt 1, then its horizontally
  stretched.
• 3) If B is negative, then it flips over the
  y-axis.
• Attached to the y vertical and intuitive
• Attached to the x horizontal and
  counter-intuitive

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1.7 Transformations of Functions

• II. What each transformation does to the graph.
• A) f(x) f(x) D
  f(x) D
• B) A f(x) A f(x)
  A f(x) . A gt 1
  0 lt A lt 1

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1.7 Transformations of Functions

• II. What each transformation does to the graph.
• C) f(x) f(x C)
  f(x C)
• D) f(Bx) f(Bx)
  f(-Bx) . B gt 1
  0 lt B lt 1

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1.7 Transformations of Functions

• III. What happens to the ordered pair (x , y)
  for shifts.
• A) f(x) D (add the D term to the y
  value)
• Example f(x) 2 (5 , 4) ?
• f(x) 3
  (5 , 4) ?
• B) A f(x) (multiply the y value by A)
• Example 3 f(x) (5 , 4) ?
• ½ f(x) (5 , 4) ?
• 2 f(x)
  (5 , 4) ?
• C) f(x C) (add C to the x value)
  change Cs sign
• Example f(x 2) (5 , 4) ?
  (subtract 2)
• f(x 3)
  (5 , 4) ? (add 3)

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1.7 Transformations of Functions

• III. What happens to the ordered pair (x , y)
  for shifts.
• D) f(Bx) or f (B(x))
• 1) If B gt 1 (divide the x value by B)
• Example f(2x) (12 , 4) ?
• f(3x) (12 , 4) ?
  
• f (4(x))
  (12 , 4) ?
• 2) If 0ltBlt1 (divide the x value by B) flip
  multiply
• Example f(½x) (12 , 4) ?
• f (¾(x)) (12 , 4) ?
• 3) If B is negative (follow the above
  rules for dividing)
• Example f(-2x) (12 , 4) ?
• f (-½(x))
  (12 , 4) ?

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1.7 Transformations of Functions
f(x) is shown below. Find the coordinates for the
following shifts.
f(x) 4 f(x) 6
(-4,6) (-1,4) (1,7 ) (2,1)
(-4,-4) (-1,-6) (1,-3) (2,-9)
f(x 4) f(x 3)
(-8,2) (-5,0) (-3,3) (-2,-3)
(-1,2) (2,0) (4,3) (5,-3)
2 f(x) ½ f(x)
-3 f(x)
(-4,4) (-1,0) (1,6) (2,-6)
(-4,1) (-1,0) (1,3/2) (2,-3/2)
(-4,-6) (-1,0) (1,-9) (2,9)
f(2x) f(½x)
f(-3(x))
(-2,2) (-1/2,0) (1/2,3) (1,-3)
(-8,2) (-2,0) (2,3) (4,-3)
(4/3,2) (1/3,0) (-1/3,3) (-2/3,-3)
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1.7 Transformations of Functions

• Identify the parent function and describe the
  sequence of transformations.

Horizontal shift eight units to the right
or y-axis!
Reflection in the x-axis, and a vertical shift of
one unit downward
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1.7 Transformations of Functions

• Identify the parent function and describe the
  sequence of transformations.
• Parent Function
• Left 2
• Horizontally compressed by a factor of 1/2

Always factor If possible!
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1.7 Transformations of Functions

• Identify the parent function and describe the
  sequence of transformations.
• Flip over y-axis and right 4
• If x is negated, factor out a negative!

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• When graphing, perform non-rigid transformations
  1st and rigid transformations last
• That means stretch / compress / reflect before
  moving left / right / up / down
• Then find a few points and perform
  transformations on those points.
• Ex Graph
• Ex Graph

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Practice

• Ex Graph
• Ex Graph

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H Dub

• 1-7 Page 80 9-12 (parts A and B only), 13-18all,
  19-39EOO