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The cube root function exists in quadrants I and III.
A. True
B. False

User Bernnabe
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1 Answer

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Final answer:

The cube root function does exist in quadrants I and III because positive numbers yield positive cube roots in Quadrant I, and negative numbers yield negative cube roots in Quadrant III. The statement is true.

Step-by-step explanation:

The cube root function indeed exists in quadrants I and III on a two-dimensional (x-y) graph. The statement is true. To understand why, consider the properties of the cube root function. First, any positive number, when subjected to a cube root, will return a positive result.

Which places its representation in Quadrant I of the Cartesian plane, where both x and y values are positive. Conversely, cube rooting a negative number will yield a negative result, which will be represented in Quadrant III where both the x and y values are negative.

This is due to the fact that the cube of a negative number is negative, and taking the cube root brings it back to a negative value.

User Pedrouan
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