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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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Step-by-step explanation:

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Step-by-step explanation:

We know that C and D lie on the line AB and BC = CD = AB. Then we need to use the distance formula and equation of the line AB to find the other two coordinates.

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Let's also find the equation of the line AB. The y-intercept we know is 2, so in y = mx + b, b = 2. The slope is (6 - 2) / (6 - 0) = 4/6 = 2/3. So the equation of the line is: y = (2/3)x + 2. Since (a, b) lines on this line, we can put in a for x and b for y: b = (2/3)a + 2. Substitute this expression in for b in the previous equation:

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b = 2/3a + 2 = (2/3) * 18 + 2 = 12 + 2 = 14

So point D has coordinates (18, 14).

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