1. Bellringer August 23rd
Graph the following equations
𝑦= 𝑥
𝑦= 𝑥 2
𝑦= 𝑥

2. Graphing techniques: Transformations
MAFS.912.F-BF.1.1

3. Transformations on Functions consist of being ________, ___________________, or reflected.
Shifted stretched /compressed

4. Assuming c is a positive constant
Adding/Subtracting a constant ___________
the function corresponds to a __________ shift that goes ____________________.
To Graph: Shift graph 𝑓 𝑥 +𝑐 c units _________
𝑓 𝑥 +𝑐 c units _________
outside
vertical
With the sign up
down

5. Assuming c is a positive constant
Adding/Subtracting a constant ___________
the function corresponds to a __________ shift that goes ____________________.
To Graph: Shift graph 𝑓 𝑥+𝑐 c units _________
𝑓 𝑥+𝑐 c units _________
inside
horizontal
opposite the sign
left
right

6. Examples:
Given the Parent function 𝑓 𝑥 = 𝑥 2 describe the shifts for the following functions
𝑔 𝑥 = 𝑥 ____________
ℎ 𝑥 = (𝑥−3) ____________
𝐹 𝑥 = (𝑥+4) 2 −2 ____________
Up 6
Right 3
Left 4 down 2

7. Horizontal and Vertical Shifts and Changes in the Domain and Range
As a function is transformed the ___________ and ____________ may also change. Consider the following: When 𝑓 𝑥 = 𝑥 the domain: _______ range: _______ However, for 𝑓 𝑥+1 = 𝑥+1 the Domain: _______ range: _______
Domain
Range
[0, ∞)
[0, ∞)
[−1, ∞)
[0, ∞)

8. Reflections
The graph of ______ is obtained by reflecting the graph of 𝑓(𝑥) about the _____.
−𝑓(𝑥)
𝑥−𝑎𝑥𝑖𝑠
𝑓(−𝑥)
y−𝑎𝑥𝑖𝑠

9. Examples: Graph the following reflections and shifts
𝑓 𝑥 = 𝑥 ________________
𝑓 𝑥+2 = 𝑥 ________________
𝑓 −𝑥+2 = −𝑥 ________________
𝑓 −𝑥+2 +1= 2−𝑥 +1 ________________
Start with the square root function
Shift left 2 units
Reflect over the y axis
Shift up 1 unit

10. Stretching and compressing the graph
Horizontal: The graph of 𝑓(𝑐𝑥) is found by:
Horizontally _____________ the graph of 𝑓(𝑥) if __________
Vertical: The graph of 𝑐𝑓(𝑥) is found by:
Vertically _____________ the graph of 𝑓(𝑥) if __________
Note: c is any positive real number.
stretching
0<𝑐<1
compressing
𝑐>1
stretching
𝑐>1
compressing
0<𝑐<1

11. Sketching the graph of a function using multiple Transformations
Graph the following : 𝑓 𝑥 = 𝑥 2 𝑓 𝑥−3 =___________ 2𝑓 𝑥−3 =___________ −2𝑓 𝑥−3 =__________
Right 3 units
Vert stretch by 2
Reflect over x-axis

12. Homework Due August 24th
TB p even,28, 32, 34, 36, 50, 54, 58, 62, 66, 70, 74 (23 problems total USE GRAPH PAPER)