Parent Function Worksheet 1



Transformation Homework Name __________________Pd. ___

Give the name of the parent function. Describe the transformation represented.

1. g(x) = x 2 – 1

2. f(x) = [pic]

3. h(x) = [pic]

4. g(x) = x3+ 3

5. g(x) = [pic]

6. f(x) = [pic]-2

7. h(x) = [pic]

8. g(x) = 3[pic]

9. h(x) = - x2 + 1

10. h(x) = [pic]

11. f(x) = [pic]

12. h(x) = 6 (x + 9)2

13. g(x) = 2(x-3)2 + 1

14. h(x) = - ½ x + 7

15. g(x) = 3(x-1)2 – 6

16. h(x) = [pic]

17. f(x) = [pic]

18. [pic]

Given the parent function and a description of the transformation, write the equation of the transformed function, f(x). Identify the domain and range of the function.

19. Absolute value—vertical shift up 5, horizontal shift right 3.

20. Radical—vertical compression by [pic]

21. Cubic—reflected over the x axis and vertical shift down 2

22. Rational—vertical stretch by 8

23. Quadratic—vertical compression by .45, horizontal shift left 8.

24. Absolute Value—reflected over the x axis and translated down 3.

25. Radical—vertical compression by a factor of [pic] & translated right

26. Linear---vertical stretch of 8 and translated up 2.

27. Cubic—translated left 1 and up 9.

28. Rational ---reflected over the x axis, translated down 3

Translate the given parent function so that the transformed function has a vertex (or critical point) at the given point.

29. Absolute value starting @ (-3, 1)

30. Quadratic starting @ (5, -6)

31. Radical starting @ (-2, 4)

32. Rational starting @ (0, 4)

33. Cubic starting @ (-2, 0)

34. Linear (0, 8) slope = ½

Identify the parent function, describe the transformation, write the equation and determine the domain and range.

35. 36.

37. 38.

39. 40.

41. 42.

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