A. The graph of the function $f(x)=\dfrac{1}{2}\sqrt[3]{x}$ is vertically shrunk by a factor $\frac{1}{2}$ the graph of the function $f(x)=\sqrt[3]{x},$ so the domain and the range of both functions are the same. This option is false.

B. The graph of the function $f(x)=\dfrac{1}{2}\sqrt[3]{x}$ is vertically shrunk by a factor $\frac{1}{2}$ the graph of the function $f(x)=\sqrt[3]{x},$ so the domain and the range of both functions are the same. This option is true.

C. The graph of the function $f(x)=\dfrac{1}{2}\sqrt[3]{(x-2)}$ is translated 2 units to the right and vertically shrunk by a factor $\frac{1}{2}$ the graph of the function $f(x)=\sqrt[3]{x},$ so their graphs are similar except the first graph is shifted right and shrunk vertically by a factor of $\frac{1}{2}.$ . This option is true.

D. The function $f(x)=\dfrac{1}{2}\sqrt{x}$ has the domain and the range all non-negative real values. The function $f(x)=\sqrt[3]{x}$ has the domain and the range all real values. So this option is false.

3 0

3 years ago