Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2b) p(x)=f(x+2)c) h(x)=-f(x)
Do Now
Unit 1 Test
• Logs – be specific! What do you need to practice more on?
• Your proof of practice can be correcting old quick checks and the recent Unit 1 test.
• Schedule a time with me if you want a retake.
Describe or draw the graph of g(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2b) p(x)=f(x+2)
Do Now
I. Domain/Input and Range/Output Relationships
LT: 2A I can identify the effect on the graph of replacing f(x) by f(x) + k, k·f(x), f(kx), and f(x +k) for specific values of k
(both positive and negative), including using technology. I can find the value of k given the graphs. I can recognize even
(symmetric about the y-axis) and odd (symmetric about the origin) functions from their graphs and algebraic expressions)
Notes Title: Function Transformations Pt. 1
Vocabulary
A Vertical shift is a translation with out rotation or distortion in the up –down direction.
A Horizontal shift is a translation with out rotation or distortion in the left -right direction.
Slide
Visual
F(x) Vertical ShiftF(x)+ k
Horizontal ShiftF(x + k)
(0,0) (0,k) (-k,0)
Parent
Function
Adding to the Range/
output
Adding to the Domain/input
Vertical Shifts: UP? DOWN?
UP for k > 0DOWN for k < 0
(0,k)
(0,-k)
Positive Number
Negative Number
Vertical ShiftF(x)-k
Vertical ShiftF(x)+ k
Horizontal ShiftF(x - k)
Horizontal shifts: LEFT? RIGHT?
RIGHT for k < 0LEFT for k > 0
(-k,0)
(k,0)
Positive NumberNegative
Number
Horizontal ShiftF(x + k)
Example 1Given that f(x)=x2, Describe the Vertical and Horizontal Shifts of g(x) =(x+1)2 - 4
Vertical Shift
Horizontal Shift
The graph of f(x) completes a vertical shift of 4 down and a horizontal shift of 1 to the left
x+1 = 0 x = -1
Use Geogebra as a visual
Example 2 The trajectory of the canon ball is shown below. Where should the canon be rolled to
in order to hit the target?
Cheat SheetQuadratic
2)( xxf Linear Absolute Value
bmxxf )( xxf )(
Square Rootxxf )( Cubic
3)( xxf
ConnectionsInput(Domain) / Output(Range)
Function
Transformation (Translation)
Horizontal Shift f(x+k)
Vertical Shift f(x) +k
Parent Function
Quadratic
Linear
Exponential
Do Now
What do you think the original parent function’s equation looked like?
Vertical Shifts: UP? DOWN?
UP for k > 0DOWN for k < 0
(0,k)
(0,-k)
Positive Number
Negative Number
Vertical ShiftF(x)-k
Vertical ShiftF(x)+ k
Horizontal ShiftF(x - k)
Horizontal shifts: LEFT? RIGHT?
RIGHT for k < 0LEFT for k > 0
(-k,0)
(k,0)
Positive NumberNegative
Number
Horizontal ShiftF(x + k)
Example 3
Name the shifts necessary to go from
to
1)3( 2 xy
4)7( 2 xy
-10 +5
Horizontal shift to
the right
Vertical shift, up
Today…
1. Translations on Parent Functions– Use your notes!
2. Goal Problem
Goal Problems (LT 2A #1)
Recall & ReproductionsIdentify the parent graph and the shifts from f(x) to g(x) :
RoutineName the shifts
necessary to go from
to
Assessment
• If you got both correct, do “Jelly”• If you got the first (graph) problem correct but
not the second one, do “Peanut”• If you got none of them correct, do “Butter”
Do Now
Active Sense-Making Recall & Reproductions
Matching Graphs and shifts
cards
Routine
Gallery Walk on the walls
Still need this.
Non-Routine
A.) Vertical & Horizontal Scale factor.
I.) Domain/Input & Range/Output Relationship
The growth of a Function is increased when the domain or range is multiplied scale factor of k.
f(kx) kf(x)
Increasing the Domain by a multiple of k
Increasing the Range by a
multiple of k
B.) Visual
I.) Domain/Input & Range/Output Relationship
Compare the rate of change
for each function
IncreasesFaster
C.) Process (ex)
I.) Domain/Input & Range/Output Relationship
D. Connections
Input(Domain) / Output(Range)
Function
Transformation (Translation)
Horizontal Shift f(x+k)
Vertical Shift f(x) +k
Transformation (Stretching)
Parent Function
Quadratic
Linear
Exponential
Goal Problems (LT 2A #1)
Recall & Reproductions
Compare between f(x) and g(x):
1.) f(x) = 4x2 ; g(x)= 2x2
2.) f(x)= (4x)2; g(x)=(2x)2
Routine
Compare function’s growth rate is increasing
faster:f(x) = 3x2
Org(x)=(3x)2