Multiple Transformations of Functions

Multiple Transformations

What happens to the parent function when multiple transformations take place?

Poll

Which transformation(s) are you feeling confident with going into this lesson?

• Horizontal translations

• Vertical translations

• Reflections

• Vertical stretching/shrinking

• Horizontal stretching/shrinking

Fill in the Blank

Given the parent function:  $f\left(x\right)=3x-4$  , the following transformations took place in this order.

Reflection over y-axis
Translation 4 units right
Vertical stretch by a factor of 2
Translation 2 units down
Reflection over x-axis

Find the resulting function  $g\left(x\right)$  =  ____________
Insert the linear expression in standard form that fills in the blank.   (no space between any characters Ex:  5x+11 ).

Fill in the Blank

Extra Practice 1:

Parent function:  $f\left(x\right)=\frac{3}{2}x+4$   
Transformations:  shift right 6; horizontal shrink by a factor of  $\frac{1}{4}$  ; reflect over y-axis

g(x) = _____________________________

Insert the linear expression in standard form that fills in the blank.   (no space between any characters Ex:  5x+11 ).

Fill in the Blank

Extra Practice 2: 

Parent function:   $f\left(x\right)=15x-9$      Transformations:  vertical shrink by a factor of  $\frac{2}{3}$   ; shift down 5; reflect over x-axis

Insert the linear expression in standard form that fills in the blank.   (no space between any characters Ex:  5x+11 ).

 

Multiple Select

Whose list of transformations is accurate? Mark all that apply.

• Lexi

• Aditya

• Cliff

• Jamie

• None of them

Open Ended

Create your own transformation list that will transform the parent function:

 $h\left(x\right)=2x-8$ ,  into  $j\left(x\right)=-x+7$  

Open Ended

Reflection: What is something new you learned today about transformations of functions?