1. PARENT FUNCTIONS Constant Function Linear (Identity) Absolute Value
Quadratic
Cubic
Square Root
Greatest Integer
Inverse

2. Constant Function
f(x) = a
where a = any #

3. Constant Function
Domain:
Range:
Parent Equation: f(x) = 2

4. x – intercept: y – intercept: None Parent Equation: f(x) = 2
Constant Function
Parent Equation: f(x) = 2
x – intercept:
y – intercept:
None

5. Table: x y -2 2 -1 1 Parent Equation: f(x) = 2
Constant Function
Table: x y -2 2 -1 1
Parent Equation: f(x) = 2
Graph Description: Horizontal Line

6. Linear Function
(Identity)
f(x) = x
Variation would be:
y = mx + b

7. Linear Function
(Identity)
Domain:
Range:
Parent Equation: f(x) = x

8. y – intercept: x – intercept: Parent Equation: f(x) = x
Linear Function
(Identity)
Parent Equation: f(x) = x
x – intercept:
y – intercept:

9. Parent Equation: f(x) = x
Linear Function
(Identity)
Table: x y -2 -1 1 2
Parent Equation: f(x) = x
Graph Description: Diagonal Line

10. Absolute Value
Function
f(x) = │x │

11. Absolute Value
Function
Parent Equation:
f(x) = │x │
Domain:
Range:

12. y – intercept: x – intercept: Parent Equation: f(x) = │x │
Absolute Value
Function
Parent Equation: f(x) = │x │
x – intercept:
y – intercept:

13. Table: x y -2 2 -1 1 Parent Equation: Graph Description: “V” - shaped
Absolute Value
Function
Table: x y -2 2 -1 1
Parent Equation:
f(x) = │x │
Graph Description: “V” - shaped

14. Quadratic Function
f(x) = x 2

15. Quadratic Function
Parent Equation:
f(x) = x 2
Domain:
Range:

16. y – intercept: x – intercept: Parent Equation: Quadratic Function
f(x) = x 2

17. Table: x y -2 4 -1 1 2 Parent Equation:
Quadratic Function
Table: x y -2 4 -1 1 2
Parent Equation:
f(x) = x 2
Graph Description: “U” - shaped

18. Cubic Function
f(x) = x 3

19. Cubic Function
Parent Equation:
f(x) = x 3
Domain:
Range:

20. y – intercept: x – intercept: Parent Equation: Cubic Function
f(x) = x 3

21. Table: x y -2 -8 -1 1 2 8 Parent Equation: Graph Description: Squiggle
Cubic Function
Table: x y -2 -8 -1 1 2 8
Parent Equation:
f(x) = x 3
Graph Description: Squiggle

22. Square Root
Function
f(x) = x

23. Square Root
Function
Parent Equation:
f(x) = x
Domain:
Range:

24. y – intercept: x – intercept: Parent Equation: Square Root Function
f(x) = x

25. Table: x y 1 4 2 9 3 16 Parent Equation: Square Root Function f(x) = x1 4 2 9 3 16
Parent Equation:
f(x) = x
Graph Description: Horizontal ½ of a Parabola

26. Inverse Function or Rational Function
(Reciprocal of x)
f(x) = 1 x

27. Inverse Function or Rational Function
(Reciprocal of x)
f(x) = 1 x
Parent Equation:
Domain:
Range:

28. Inverse Function or Rational Function
(Reciprocal of x)
f(x) = 1 x
Parent Equation:
x – intercept:
y – intercept:

29. Inverse Function or Rational Function
(Reciprocal of x)
Table: x y -2
-0.5 -1
Error 1 2
0.5
f(x) = 1 x
Parent Equation:
Graph Description: Opposite “L” Curves in 1st and 3rd Quadrants

30. Step Function
(Greatest Integer)
f(x) = [x]

31. Domain: Range: Parent Equation: Step Function (Greatest Integer)
f(x) = [x]
Domain:
Range:

32. y – intercept: x – intercept: Parent Equation: Step Function
(Greatest Integer)
Parent Equation:
f(x) = [x]
y – intercept:
x – intercept:

33. Table: x y Parent Equation: Graph Description: Stair Steps
Step Function
(Greatest Integer)
Table: x y -2 -1 1 2
Parent Equation:
f(x) = [x]
Graph Description: Stair Steps

35. Inverse Squared
Function
(Reciprocal of x 2)
f(x) = 1
x 2

36. Parent Equation: Domain: Range: Inverse Squared Function
(Reciprocal of x 2)
f(x) = 1
x 2
Parent Equation:
Domain:
Range:

37. y – intercept: x – intercept: Parent Equation: Inverse Squared
Function
(Reciprocal of x 2)
f(x) = 1
x 2
Parent Equation:
x – intercept:
y – intercept:

38. Table: x y -2 0.25 -1 1 Error 2 Parent Equation: Inverse Squared
Function
(Reciprocal of x 2)
Table: x y -2
0.25 -1 1
Error 2
f(x) = 1
x 2
Parent Equation:
Graph Description: Symmetrical “L” Curves in 1st and 2nd Quadrants