1. Function Notation
Transformations

2. 𝑓 𝑥 “F of x"
𝑓 𝑥 is a substitute for “y.” 𝑓 𝑥 represents the output when using x as the input.
The function described by ƒ(x) = 5x + 3 is the same as the function described by y = 5x + 3.

3. Evaluating Functions Just plugging it in 𝑓 𝑥 =5𝑥+3 𝑓 3 =
Find the following outputs for each function.
𝑓 𝑥 =5𝑥+3
Just plugging it in
𝑓 3 =
5 3 +3=15+3=18
𝑓 0 =
5 0 +3=0+3=3
𝑓 −5 =
5 −5 +3=−25+3=−22

4. Transforming 𝑓(𝑥) 𝑓 𝑥 +𝑘 Vertical Shift: Up(+) or down(-) k units
𝑓 𝑥+𝑘
Horizontal Shift: Left(+) or right(-) k units
𝑘𝑓 𝑥
Stretch
−𝑓 𝑥
Flip

5. Example Function x y -2 4 -1 1 2 x y -2 9 -1 6 5 1 2 𝑓 𝑥 = 𝑥 2 𝑓 𝑥 +5=
𝑥 2 +5
(Standard Function)
(Vertical Shift) x y -2 4 -1 1 2 x y -2 9 -1 6 5 1 2

6. Example Function x y -7 4 -6 1 -5 -4 -3 x y -2 20 -1 5 1 2 𝑓 𝑥+5 =
(𝑥+5) 2
5𝑓 𝑥 =
5𝑥 2
(Horizontal Shift)
(Stretch) x y -7 4 -6 1 -5 -4 -3 x y -2 20 -1 5 1 2

7. Example Function 2 x y -2 2 -1 1 x y -2 -4 -1 1 2 4 𝑓 𝑥 =|𝑥| −2𝑓 𝑥 =
−2|𝑥|
Standard Function
Stretch and Flip x y -2 2 -1 1 x y -2 -4 -1 1 2 4

8. Example Function 2 x y 1 2 3 4 5 x y -2 -1 -3 1 2 𝑓 𝑥−3 = |𝑥−3|
𝑓 𝑥 −3=
𝑥 −3
Horizontal Shift
Vertical Shift x y 1 2 3 4 5 x y -2 -1 -3 1 2

9. Multiple Shifts x y 1 2 1.4 3 1.7 4 x y -3 -5 -2 -4 -1 -3.6 -3.3 1
𝑥+3 −5
𝑓 𝑥 = 𝑥
𝑓 𝑥+3 −5=
Standard Function
Horizontal and Vertical Shifts x y 1 2
1.4 3
1.7 4 x y -3 -5 -2 -4 -1
-3.6
-3.3 1

10. Multiple Shifts x y 2 1 -3 -5.1 3 -6.7 4 -8 −5𝑓 𝑥 +2= −5 𝑥 +2
−5 𝑥 +2
Stretch and Vertical Shift x y 2 1 -3
-5.1 3
-6.7 4 -8