1. L AST MATHEMATICIAN STANDING Review 1.4-1.6

2. P ROBLEM 1 Find f(g(x)) and f(f(x)).

3. P ROBLEM 1 - ANSWERS Find f(g(x)) and f(f(x)).

4. P ROBLEM 2 Find f(g(x)) and its domain.

5. P ROBLEM 2 Find f(g(x)) and its domain. Domain of f(g(x)) is ( 2, ∞ )

6. P ROBLEM 3 f(x) = g(x) =

7. P ROBLEM 3 f(x) = g(x) =

8. P ROBLEM 4 g(x) = f(x) =

9. P ROBLEM 4 g(x) = f(x) =

10. P ROBLEM 5 Find the inverse of h(x).

11. P ROBLEM 5 Find the inverse of h(x).

12. P ROBLEM 6 Find g(f(-1)).

13. P ROBLEM 6 Find g(f(-1)).

14. For the remaining problems, give the basic function and all the vertical and horizontal transformations in the correct order! Be sure to mention where the horizontal and vertical asymptotes are.

15. P ROBLEM 7

16. Basic Function is Horizontal SHIFT right 6 Horizontal shrink BAFO 1/3rd

17. P ROBLEM 8

18. Basic Function is Horizontal SHIFT right 4 Vertical SHIFT up 3

19. P ROBLEM 9

20. Basic Function is Vertical STRECTH BAFO 2 Vertical SHIFT up 7 HA is at y = 7

21. P ROBLEM 10

22. Basic Function is Reflection over the x-axis Vertical SHIFT up 6 Horizontal SHRINK BAFO 1/4 th VA is at X=0

23. P ROBLEM 11

24. Basic Function is Reflection over the y-axis Horizontal SHRINK BAFO 1/2 Vertical SHIFT up 1

25. P ROBLEM 12

26. Basic Function is Horizontal SHIFT left 5 Horizontal SHRINK BAFO 1/3rd Reflection over the y-axis

27. P ROBLEM 13

28. Basic Function is Horizontal STRETCH BAFO 3 Vertical STRETCH BAFO 2 Reflection over the x-axis Vertical SHIFT down 4

29. P ROBLEM 14

30. Basic Function is Reflection over the y-axis Vertical SHRINK BAFO 1/2 Vertical SHIFT down 7

31. P ROBLEM 15

32. Basic Function is Horizontal SHIFT right 4 Horizontal STRETCH BAFO 2 Vertical SHIFT up 2

33. P ROBLEM 16 Find and its domain.

34. P ROBLEM 16 Find and its domain. Domain of inverse is [ 0, ∞ )