1. Project 1: Graphing Functions
Name: Ahmad Al-Rashid
ID:
Section:106
Pre-Calculus
Instructor: Dr. Nader Green

2. Linear Function F(x) = X+4 F(x) = -X F(x) = X-4 F(x) = X
Parent function: F(x) = X
Shifted up 4 units: F(x) = X+4
Shifted down 4 units: F(x) = X-4
Shifted right 4 units: F(x) = (X-4)
Shifted left 4 units: F(x) = (X+4)
Reflected: F(x) = -X

3. Parent function: F(x) = 𝑋 2 Shifted up 2 units: F(x) = 𝑋 2 +2
Quadratic Function
F(x) = 𝑋 2 +2
F(x) =( 𝑋+2) 2
F(x) = 𝑋 2
F(x) = (𝑋−2) 2
F(x) = 𝑋 2−2
F(x) =- 𝑋 2
Parent function: F(x) = 𝑋 2
Shifted up 2 units: F(x) = 𝑋 2 +2
Shifted down 2 units: F(x) = 𝑋 2 -2
Shifted right 2 units: F(x) = ( 𝑋 2 -2)
Shifted left 2 units: F(x) = ( 𝑋 2 +2)
Reflected: F(x) = - 𝑋 2

4. Absolute Value Function
F(x) = |X|+4
F(x) = (|X|-4)
F(x) = (|X|+4
F(x) = |X|
F(x) = |X|-4
F(x) = -|X|
Parent function: F(x) = |X|
Shifted up 4 units: F(x) = |X|+4
Shifted down 4 units: F(x) = |X|-4
Shifted right 4 units: F(x) = (|X|-4)
Shifted left 4 units: F(x) = (|X|+4)
Reflected: F(x) = -|X|

5. Square Root Function F(x) = X +4 F(x) = ( X +4) F(x) = X
Parent function: F(x) = X
Shifted up 4 units: F(x) = X +4
Shifted down 4 units: F(x) = X -4
Shifted right 34units: F(x) = ( X -4)
Shifted left 4 units: F(x) = ( X +4)
Reflected: F(x) = - X

6. Exponential Function F(x) = 2 𝑥 +4 F(x) = 2 𝑥 F(x) = ( 2 𝑥 -4)
Parent function: F(x) = 2 𝑥
Shifted up 4 units: F(x) = 2 𝑥 +4
Shifted down 4 units: F(x) = 2 𝑥 -4
Shifted right 4 units: F(x) = ( 2 𝑥 -4)
Shifted left 4 units: F(x) = ( 2 𝑥 +4)
Reflected: F(x) = - 2 𝑥

7. Reciprocal Function F(x) = 1 𝑥 + 4 F(x) = ( 1 𝑥 + 4) F(x) = - 1 𝑥
Parent function: F(x) = 1 𝑥
Shifted up 4 units: F(x) = 1 𝑥 + 4
Shifted down 4 units: F(x) = 1 𝑥 - 4
Shifted right 4 units: F(x) = ( 1 𝑥 - 4)
Shifted left 4 units: F(x) = ( 1 𝑥 + 4)
Reflected: F(x) = - 1 𝑥

8. Cubic Function
F(x) = 𝑥 3 +4
F(x) = ( 𝑥 3 +4)
F(x) = 𝑥 3
F(x) = ( 𝑥 3 -4)
F(x) = - 𝑥 3
F(x) = 𝑥 3 -4
Parent function: F(x) = 𝑥 3
Shifted up 4 units: F(x) = 𝑥 3 +4
Shifted down 4 units: F(x) = 𝑥 3 -4
Shifted right 4 units: F(x) = ( 𝑥 3 -4)
Shifted left 4 units: F(x) = ( 𝑥 3 +4)
Reflected: F(x) = - 𝑥 3

9. Trigonometric Function for Sine
Parent function: F(x) = Sin(X)
Shifted up 2 units: F(x) = Sin(X)+2
Shifted down 2 units: F(x) = Sin(X)-2
Shifted right 2 units: F(x) = (Sin(X)-2)
Shifted left 2 units: F(x) = (Sin(X)+2)
Reflected: F(x) = -Sin(X)

10. Trigonometric Function for Cosine
Parent function: F(x) = Cos(X)
Shifted up 2 units: F(x) = Cos(X)+2
Shifted down 2 units: F(x) = Cos(X)-2
Shifted right 2 units: F(x) = (Cos(X)-2)
Shifted left 2 units: F(x) = (Cos(X)+2)
Reflected: F(x) = - Cos(X)

11. Trigonometric Function for Tan
Parent function: F(x) = Tan(X)
Shifted up 3 units: F(x) = Tan(X)+2
Shifted down 3 units: F(x) = Tan(X)-2
Shifted right 3 units: F(x) = (Tan(X)-2)
Shifted left 3 units: F(x) = (Tan(X)+2)
Reflected: F(x) = - Tan(X)