Answer:
B, C
Step-by-step explanation:
Consider all options:
A. The graph of the function [tex]f(x)=\dfrac{1}{2}\sqrt[3]{x}[/tex] is vertically shrunk by a factor [tex]\frac{1}{2}[/tex] the graph of the function [tex]f(x)=\sqrt[3]{x},[/tex] so the domain and the range of both functions are the same. This option is false.
B. The graph of the function [tex]f(x)=\dfrac{1}{2}\sqrt[3]{x}[/tex] is vertically shrunk by a factor [tex]\frac{1}{2}[/tex] the graph of the function [tex]f(x)=\sqrt[3]{x},[/tex] so the domain and the range of both functions are the same. This option is true.
C. The graph of the function [tex]f(x)=\dfrac{1}{2}\sqrt[3]{(x-2)}[/tex] is translated 2 units to the right and vertically shrunk by a factor [tex]\frac{1}{2}[/tex] the graph of the function [tex]f(x)=\sqrt[3]{x},[/tex] so their graphs are similar except the first graph is shifted right and shrunk vertically by a factor of [tex]\frac{1}{2}.[/tex]. This option is true.
D. The function [tex]f(x)=\dfrac{1}{2}\sqrt{x}[/tex] has the domain and the range all non-negative real values. The function [tex]f(x)=\sqrt[3]{x}[/tex] has the domain and the range all real values. So this option is false.
