Post on 30-Sep-2020
transcript
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