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)+2 b)...

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