Question

Which of the following statements are true?

Answer 1

B, C

Explanation:

Consider all options:

A. The graph of the function
`f(x)=(1)/(2)\sqrt[3]{x}` is vertically shrunk by a factor
`(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)=(1)/(2)\sqrt[3]{x}` is vertically shrunk by a factor
`(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)=(1)/(2)\sqrt[3]{(x-2)}` is translated 2 units to the right and vertically shrunk by a factor
`(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
`(1)/(2).`. This option is true.

D. The function
`f(x)=(1)/(2)√(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.