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Functions. Transformation of Functions. AIM: Transform a parent function in order to sketch a function. Remember. Identify the functions of the graphs below:. Square Root. Absolute Value. Q uadratic. Linear. f (x) = x. f (x) = | x |. f (x) =. f (x) = x 2.

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functions

Functions

Transformation of Functions

remember

AIM: Transform a parent function in order to sketch a function.

Remember
  • Identify the functions of the graphs below:

Square Root

Absolute Value

Quadratic

Linear

f(x) = x

f(x) = |x|

f(x) =

f(x) = x2

transformed

AIM: Transform a parent function in order to sketch a function.

Transformed
  • Each of the prior graphs are called parent functions
  • We can use a parent function to quickly sketch ‘babies’

f(x) = x

f(x) = |x|

f(x) =

f(x) = x2

translation

AIM: Transform a parent function in order to sketch a function.

Translation
  • Each parent function can slide

f(x) = x2 - 3

f(x) = (x + 3)2

f(x) = x2

f(x) = x2

f(x) = x2 + 3

f(x) = (x - 3)2

slide the function

AIM: Transform a parent function in order to sketch a function.

SLIDE THE FUNCTION

y = ( x+ c) + d

VERTICAL SHIFT

+ up

- down

HORIZONTAL SHIFT

+left

-right

reflection

AIM: Transform a parent function in order to sketch a function.

Reflection
  • Each parent function can flip

f(x) = √-x

f(x) = √x

f(x) = √x

f(x) = - √x

flip the function

AIM: Transform a parent function in order to sketch a function.

Flip THE FUNCTION

y = -(-x+ c) + d

REFLECT

over the x axis

VERTICAL SHIFT

+ up

- down

HORIZONTAL SHIFT

+ down

- up

REFLECT

over the y axis

dilation

AIM: Transform a parent function in order to sketch a function.

Dilation
  • Each parent function can change size

f(x) = 0.5x2

f(x) = (0.5x)2

f(x) = x2

f(x) = x2

f(x) = (2x)2

f(x) = 2x2

stretch the function

AIM: Transform a parent function in order to sketch a function.

Stretch THE FUNCTION

y = - a (-bx+ c) + d

REFLECT

over the x axis

VERTICAL

a > 1 stretches

0 < a < 1 flattens

VERTICAL SHIFT

+ up

- down

HORIZONTAL SHIFT

+ left

- right

REFLECT

over the y axis

HORIZONTAL

b > 1 narrow

0 < b < 1 widens

slide10

AIM: Transform a parent function in order to sketch a function.

TRY
  • Describe f(x) = -2(x + 3)2 - 1

f(x) = (x + 3)2

f(x) = x2

f(x) = 2(x+3)2

a parabola

that shifts to the left 3 units,

is stretched vertically by a factor of 2,

flipped over the x axis,

and brought down 1 unit.

f(x) = -2(x+3)2

f(x) = -2(x+3)2