Name ________________________________________________________ Date _______________________

Rules for Algebraic Transformations Given a parent function f(x), the transformation of the function is given by:

Each of the letters a, h, and k have a job.

a _____________________________________________________________________

h _____________________________________________________________________

k _____________________________________________________________________

When multiple transformations are happening on the same function, we

have to apply those transformations in a specific order, otherwise it doesn’t work out

quite right!

1st - ______________________________ 2nd - ______________________________

(In other words, we deal with the multiplication before addition/subtraction – just like in order of operations.)

Example 1… Describe each combined transformation, in the correct order.

a. f(x – 2) + 3 b. ½ g(x) + 3

c. -2g(x) – 7 d. 3h(x – 4) + 1

Example 2… Using the graph of f(x) on the left, graph the transformation t(x) = f(x – 2) + 3.

t(x) = a∙f(x – h) + k

ALGEBRAIC TRANSFORMATIONS

khxfaxt )()(

Order of operation for transformations: 5)2(3)( 2 xxf 324

1)( xxg

1. (a) Vertical stretch/shrink (effects y value) vertical stretch x3 vertical shrink x 1/4

2. (k) Vertical translation up/down (effects y value) translating up 5 translates down 3

3. ( a) Reflection ? reflects across x axis

4. (h) Horizontal shift (effects x value) horizontal shift to the right 2 horizontal shift to the left 2

Vertical stretch when a > 1

Vertical shrink when 0 < a < 1

If a is negative the

graph reflects(flips).

-h horizontal translation right

+h horizontal translation left

+ k vertical translation up

-k vertical translation down