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tatiyna
3 years ago
12

Which of the following statements are true?

Mathematics
1 answer:
Eduardwww [97]3 years ago
3 0

Answer:

B, C

Step-by-step explanation:

Consider all options:

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.

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