We performed the following operations:
[tex]f(x)=\sqrt[3]{x}\mapsto g(x)=2\sqrt[3]{x}=2f(x)[/tex]
If you multiply the parent function by a constant, you get a vertical stretch if the constant is greater than 1, a vertical compression if the constant is between 0 and 1. In this case the constant is 2, so we have a vertical stretch.
[tex]g(x)=2\sqrt[3]{x}\mapsto h(x)=-2\sqrt[3]{x}=-g(x)[/tex]
If you change the sign of a function, you reflect its graph across the x axis.
[tex]h(x)=-2\sqrt[3]{x}\mapsto m(x)=-2\sqrt[3]{x}-1=h(x)-1[/tex]
If you add a constant to a function, you translate its graph vertically. If the constant is positive, you translate upwards, otherwise you translate downwards. In this case, the constant is -1, so you translate 1 unit down.
