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

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.