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Which of the following describes the function x3 − 8? (10 points)


a. The degree of the function is odd, so the ends of the graph continue in opposite directions. Because the leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.
b. The degree of the function is odd, so the ends of the graph continue in the same direction. Because the leading coefficient is negative, the left side of the graph continues down the coordinate plane and the right side also continues downward.
c. The degree of the function is odd, so the ends of the graph continue in opposite directions. Because the leading coefficient is negative, the left side of the graph continues up the coordinate plane and the right side continues downward.
d. The degree of the function is odd, so the ends of the graph continue in the same direction. Because the leading coefficient is positive, the left side of the graph continues up the coordinate plane and the right side continues upward.

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Answer:

a. The degree of the function is odd, so the ends of the graph continue in opposite directions. Because the leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.

Step-by-step explanation:

The given cubic polynomial function is

[tex]f(x) = {x}^{3} - 8[/tex]

The degree of this function is odd because 3 is an odd number.

Therefore the ends of the graph, continue in opposite direction.

As x-values gets bigger and bigger negatively, the graph continues down on the Left.

As x-values gets bigger and bigger positively, the graph continues up on the right.

Therefore the correct option is A.

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