Turn homework into the box-staple together and make sure both names are on sheet!! Sckett

Turn homework into the box-staple together and make sure

both names are on sheet!!

Sckett

Transformation of Functions

Linear Function f(x) = x

The squaring function

2)( xxf

xxf )(The absolute value function

Absolute value- distance from zerofor order of operations works like ( )

3)( xxf

The cubing function

Vertical shifts up or down

Vertical Translation ( ) outsidey = x+ b shifted up b units;

y = x b shifted down b units.

2( )f x x2( ) 3f x x

2( ) 2f x x

Horizontal shifts left or right

Horizontal Translation(inside) BACKWARDS

y = (x d) shifted right d units;

y = (x + d) shifted left d units.

22y x 22y x

2( )f x x

Use the basic graph to sketch the following:

2( ) 5f x x 3( ) ( 2)f x x

( ) 3f x x

Combining a vertical & horizontal shift

• Example of function that is shifted down 4 units and right 6 units from the original function.

( ) 6

)

4

( ,

g x x

f x x

Parent Functions

y = /x/ y = x

y = x2 y = x3

Vertical shifts ( ) ± outside( ) + up ( ) - down

Horizontal shifts (±inside ) ( + left ) ( - right)

Reflections• The graph of f(x) is the reflection of the

graph of f(x) across the x-axis. (fold at x axis-flips it up and down)

Use the basic graph to sketch the following:

2( )f x x|| xy

Vertical Stretching and ShrinkingThe graph of af(x) can be obtained from the graph of f(x) by

stretching vertically for |a| > 1, or skinnershrinking vertically for 0 < |a| < 1. fatter

Multiply outside of ()

VERTICAL STRETCH (SHRINK)

2( ) 3 4f x x

2( ) 4f x x

21( ) 42

f x x

Horizontal Stretching or ShrinkingThe graph of y = (cx)

shrinking horizontally for |c| > 1, or skinnerstretching horizontally for 0< |c|< 1. fatter

Multiply inside of ()

18

Which Way Will You Shift? 

1. f(x) + a 2. f(x - a) 3. f(x)*a 4. f(x + a) 5. f(x) - a

A) shift down a units  B) shift right a units  C) shift left a units  D) shift up a units  E) turn upside down  F) none of these

Matching -- match the letter of the list on the right with the function on the left.

Horizontal stretch & shrink

2( ) (3 ) 4g x x

2( ) 4f x x

21( ) ( ) 43

f x x

CHEAT SHEET• y = 3/2x + 1/ + 4

– Left 1– Shrinking horizontal by

2– Stretching vertical by 3– Up 4

• y = -3/-2x -1/ - 4• Right 1• Stretching's horizontal

by 2• Shrinking vertical by 3• Down 4