A3 2.5a Common GraphsTransformations and

ReflectionsHomework: p. 282-283 1-9,

17-25, 45-47, 67-73, 81-89 all odd!

Introducing the Common Functions

Constant Function:graph:domain:range:inc/dec/con:odd/even:

Identity Function:graph:domain:range:inc/dec/con:odd/even:

Introducing the Common FunctionsAbsolute Value Function:

graph:domain:range:inc/dec/con:odd/even:

Square Root Function:graph:domain:range:inc/dec/con:odd/even:

Introducing the Common Functions

Standard Quadratic Function:graph:domain:range:inc/dec/con:odd/even:

Standard Cubing Function:graph:domain:range:inc/dec/con:odd/even:

Introducing the Common Functions

And the last one…Cube Root Function:

graph:domain:range:inc/dec/con:odd/even:

Now transformations…Vertical Shifts:

Horizontal Shifts:

General Rule of Thumb: “outside the function” = vertical change“inside the function” = horizontal change

( )

( )

y f x c

y f x c

( )

( )

y f x c

y f x c

Guided PracticeDescribe the transformations from f(x) to g(x). Graph the original and the transformed function. 2( )f x x 2( ) ( 1) 3g x x

( )f x x ( ) ( 1) 2g x x

And now…Reflections!About the x-axis (outside the function)

About the y-axis (inside the function)

Managing the math: reflection about the x-axis : distribute

the negative to every value in the functionreflection about the y-axis : “run” a ( –

x) through the function

( )y f x

( )y f x

Guided PracticeDescribe the transformations on :

( )f x x

( ) 4 2h x x

( ) 3 4g x x

Whiteboard Problems: 1. Describe the changes of to

2. Describe the changes of to

2( )f x x2( ) ( 3) 5g x x

3( )f x x3( ) ( 5) 2g x x