1. When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal shift from a vertical shift?

2. When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal stretch from a vertical stretch?

3. When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal compression from a vertical compression?

4. When examining the formula of a function that is the result of multiple transformations, how can you tell a reflection with respect to the x-axis from a reflection with respect to the y-axis?

5. How can you determine whether a function is odd or even from the formula of the function?

6. Write a formula for the function obtained when the graph of [latex]f\left(x\right)=\sqrt{x}[/latex] is shifted up 1 unit and to the left 2 units.

7. Write a formula for the function obtained when the graph of [latex]f\left(x\right)=|x|[/latex]
is shifted down 3 units and to the right 1 unit.

8. Write a formula for the function obtained when the graph of [latex]f\left(x\right)=\frac{1}{x}[/latex] is shifted down 4 units and to the right 3 units.

9. Write a formula for the function obtained when the graph of [latex]f\left(x\right)=\frac{1}{{x}^{2}}[/latex] is shifted up 2 units and to the left 4 units.

For the following exercises, describe how the graph of the function is a transformation of the graph of the original function [latex]f[/latex].

10. [latex]y=f\left(x - 49\right)[/latex]

11. [latex]y=f\left(x+43\right)[/latex]

12. [latex]y=f\left(x+3\right)[/latex]

13. [latex]y=f\left(x - 4\right)[/latex]

14. [latex]y=f\left(x\right)+5[/latex]

15. [latex]y=f\left(x\right)+8[/latex]

16. [latex]y=f\left(x\right)-2[/latex]

17. [latex]y=f\left(x\right)-7[/latex]

18. [latex]y=f\left(x - 2\right)+3[/latex]

19. [latex]y=f\left(x+4\right)-1[/latex]

For the following exercises, determine the interval(s) on which the function is increasing and decreasing.

20. [latex]f\left(x\right)=4{\left(x+1\right)}^{2}-5[/latex]

21. [latex]g\left(x\right)=5{\left(x+3\right)}^{2}-2[/latex]

22. [latex]a\left(x\right)=\sqrt{-x+4}[/latex]

23. [latex]k\left(x\right)=-3\sqrt{x}-1[/latex]

For the following exercises, use the graph of [latex]f\left(x\right)={2}^{x}[/latex] to sketch a graph of each transformation of [latex]f\left(x\right)[/latex].

24. [latex]g\left(x\right)={2}^{x}+1[/latex]

25. [latex]h\left(x\right)={2}^{x}-3[/latex]

26. [latex]w\left(x\right)={2}^{x - 1}[/latex]

For the following exercises, sketch a graph of the function as a transformation of the graph of one of the toolkit functions.

27. [latex]f\left(t\right)={\left(t+1\right)}^{2}-3[/latex]

28. [latex]h\left(x\right)=|x - 1|+4[/latex]

29. [latex]k\left(x\right)={\left(x - 2\right)}^{3}-1[/latex]

30. [latex]m\left(t\right)=3+\sqrt{t+2}[/latex]

31. Tabular representations for the functions [latex]f,g[/latex], and [latex]h[/latex] are given below. Write [latex]g\left(x\right)[/latex] and [latex]h\left(x\right)[/latex] as transformations of [latex]f\left(x\right)[/latex].

[latex]x[/latex]	−1	0	1	2	3
[latex]g\left(x\right)[/latex]	−2	−1	−3	1	2

[latex]x[/latex]	−2	−1	0	1	2
[latex]h\left(x\right)[/latex]	−1	0	−2	2	3

32. Tabular representations for the functions [latex]f,g[/latex], and [latex]h[/latex] are given below. Write [latex]g\left(x\right)[/latex] and [latex]h\left(x\right)[/latex] as transformations of [latex]f\left(x\right)[/latex].

[latex]x[/latex]	−2	−1	0	1	2
[latex]f\left(x\right)[/latex]	−1	−3	4	2	1

[latex]x[/latex]	−3	−2	−1	0	1
[latex]g\left(x\right)[/latex]	−1	−3	4	2	1

[latex]x[/latex]	−2	−1	0	1	2
[latex]h\left(x\right)[/latex]	−2	−4	3	1	0

For the following exercises, write an equation for each graphed function by using transformations of the graphs of one of the toolkit functions.

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For the following exercises, use the graphs of transformations of the square root function to find a formula for each of the functions.

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For the following exercises, use the graphs of the transformed toolkit functions to write a formula for each of the resulting functions.

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For the following exercises, determine whether the function is odd, even, or neither.

For the following exercises, describe how the graph of each function is a transformation of the graph of the original function [latex]f[/latex].

For the following exercises, write a formula for the function [latex]g[/latex] that results when the graph of a given toolkit function is transformed as described.