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Which best explains why Irving sets "The Adventure of the Mysterious Stranger" in a land of "masks and gondolas"?

A. The setting is symbolic of the idea that a life of quiet study is the ideal pursuit.
B. The setting is symbolic of the idea that innocence cannot be outgrown.
C. The setting is symbolic of the idea that ease and affluence are available to all.
D. The setting is symbolic of the idea that appearances can be deceiving.

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Read the lines from "The Tide Rises, The Tide Falls."

"Darkness settles on roofs and walls,
But the sea, the sea in darkness calls;"

The imagery in these lines evokes a sense of:

A. laziness
B. fear
C. mystery
D. despair

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Solve for x.

3x = 6x - 2

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What is the range of the translated function?

A. {y | y < 0}
B. {y | y ≥ 0}
C. {y | y is a natural number}
D. {y | y is a real number}



Answer :

GinnyAnswer
To determine the range of a vertical translation of the function [tex]\( y = \sqrt[3]{x} \)[/tex], we need to understand both the nature of the original function and how vertical translations affect it.

1. Original Function [tex]\( y = \sqrt[3]{x} \)[/tex]:
- The cube root function, [tex]\( y = \sqrt[3]{x} \)[/tex], is defined for all real numbers [tex]\( x \)[/tex].
- This means that for any real number [tex]\( y \)[/tex], there is some real number [tex]\( x \)[/tex] such that [tex]\( y = \sqrt[3]{x} \)[/tex].
- Therefore, the range of [tex]\( y = \sqrt[3]{x} \)[/tex] is all real numbers, i.e., [tex]\(\{ y \mid y \text{ is a real number}\}\)[/tex].

2. Vertical Translation:
- A vertical translation shifts the graph of a function up or down without changing its basic shape.
- Mathematically, a vertical translation is of the form [tex]\( y = \sqrt[3]{x} + k \)[/tex], where [tex]\( k \)[/tex] is a constant.
- Shifting the function [tex]\( y = \sqrt[3]{x} \)[/tex] vertically by [tex]\( k \)[/tex] units still allows [tex]\( y \)[/tex] to take any real value, because for every [tex]\( y \)[/tex] in the original function, [tex]\( y - k \)[/tex] would also cover all real values.

Hence, the range of the translated function remains unchanged and includes all real numbers.

Therefore, the range of a vertical translation of [tex]\( y = \sqrt[3]{x} \)[/tex] is:
[tex]\(\{ y \mid y \text{ is a real number} \}\)[/tex].

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