1. PARENT FUNCTIONS Constant Function Inverse
Linear (Identity) Inverse Squared
Absolute Value Exponential
Quadratic Logarithmic
Cubic Sine
Square Root Cosine
Signum Greatest Integer

2. Parent Functions Menu Constant Function Inverse or Rational
1) Click on this Button to View All of the Parent Functions. or
2) Click on a Specific Function Below for the Properties.
3) Use the button to return to this menu.
Constant Function Inverse or Rational
Linear (Identity) Inverse Squared
Absolute Value Exponential
Quadratic Logarithmic
Cubic Sine
Square Root Cosine
Signum Greatest Integer

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

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

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

6. 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

7. Linear Function
(Identity)
f(x) = x

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

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

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

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

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

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

14. 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

15. Quadratic Function
f(x) = x 2

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

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

18. 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

19. Cubic Function
f(x) = x 3

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

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

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

23. Square Root
Function
f(x) = x

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

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

26. 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

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

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

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

30. 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

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

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

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

34. 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

35. Exponential Function
b = base and
x = exponent

36. Exponential Function
Parent Equation:
f(x) = 2x
Domain:
Range:

37. y – intercept: x – intercept: Parent Equation: Exponential Function
f(x) = 2x
y – intercept:
x – intercept:

38. Table: x y -2 0.25 -1 0.5 1 2 4 Parent Equation: Exponential Function1 2 4
Parent Equation:
f(x) = 2x
Graph Description: Backwards “L” Curves

39. Logarithmic Function
f(x) = log x

40. Logarithmic Function
Parent Equation:
f(x) = log x
Domain:
Range:

41. y – intercept: x – intercept: Parent Equation: Logarithmic Function
f(x) = log x
x – intercept:
y – intercept:

42. Table: x y -2 Error -1 1 2 0.301 Parent Equation: Logarithmic Function1 2
0.301
Parent Equation:
f(x) = log x
Graph Description: Upside Down “L” curve in 1st and 4th Quadrant

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

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

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

46. 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

47. Signum Function

48. Signum Function
Parent Equation:
Domain:
Range:

49. Signum Function
Parent Equation:
x – intercept:
y – intercept:

50. Table: x y Signum Function Parent Equation:-2 -1 1 2
Parent Equation:
Graph Description: Left and Right Arrows Opposite Directions

51. Sine Function
f(x) = sin x

52. Sine Function
Parent Equation:
f(x) = sin x
Domain:
Range:

53. y – intercept: x – intercept: Parent Equation: Sine Function
f(x) = sin x
x – intercept:
y – intercept:

54. Table: x y Sine Function Parent Equation: f(x) = sin x-2 -1 1
0.8415 2
0.9093
Parent Equation:
f(x) = sin x
Graph Description: Wavy, above and below x-axis with y-int at (0, 0)

55. Cosine Function
f(x) = cos x

56. Cosine Function
Parent Equation:
f(x) = cos x
Domain:
Range:

57. Cosine Function
f(x) = cos x
y – intercept:
x – intercept:

58. Table: x y Cosine Function Parent Equation: f(x) = cos x-2 -1
0.5403 1 2
Parent Equation:
f(x) = cos x
Graph Description: Wavy, above and below x-axis with y-int at (0, 1)