NOTES
Transformations of Linear Functions
Name: _______________________
Date: _____________
Vocabulary:





Family of Functions: _____________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Parent Function: ________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Translation: ____________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Rotation: ______________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Reflection: _____________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
1. Graph the following equations in 4 different colors
1.
2.
3.
4.
𝑦 = 2𝑥
𝑦 = 2𝑥 + 6
𝑦 = 2𝑥 − 3
𝑦 = 2𝑥 − 5
2. What do you notice about the graphs?
____________________________________________________________________________
3. How does changing the y-intercept affect the graph?
When b increases, the graph is ____________________________________________________.
When b decreases, the graph is ____________________________________________________.
4. Graph the following equations in 4 different colors
1.
2.
3.
4.
𝑦 = 3𝑥
𝑦 = −3𝑥
𝑦=𝑥
𝑦 = −𝑥
5. What do you notice happens if your slope
is negative?
6. Graph the following equations in 4 different colors
1. 𝑦 = 2𝑥
2. 𝑦 = 𝑥
1
3. 𝑦 = 𝑥
2
4. 𝑦 = 4𝑥
7. What do you notice about the graphs?
____________________________________
____________________________________
8. How does changing the slope affect the graph?
__________________________________________________________________________________
Describe transformations from the graph of f(x) to g(x).
1. 𝑓(𝑥) = 𝑥
𝑔(𝑥) = 2𝑥 − 3
________________________________________________
2. 𝑓(𝑥) = 𝑥
𝑔(𝑥) = −𝑥 + 2
________________________________________________
3. 𝑓(𝑥) = 2𝑥 + 2
𝑔(𝑥) = 5𝑥 − 3
________________________________________________
4. 𝑓(𝑥) = 𝑥 − 4
1
𝑔(𝑥) = − 2 𝑥 + 2
________________________________________________
Given: f (x) = 2x + 1
Graph the indicated transformation.
5. shift 2 units up
6. reflect across the y-axis
Write the transformed/translated function.
7. f (x) = 2x + 8; shifted 4 units down.
8. f (x) = x – 2; reflection across the y-axis.
9. f (x) = 11x + 10; shifted 3 units up
10. f (x) = –10x + 1; reflection across the y-axis.