Which of the following describes the function x3 − 8?

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.

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:

Given : Function [tex]x^3-8[/tex]

We have to choose out of given options that correctly describes the given function [tex]x^3-8[/tex].

Consider the given function [tex]x^3-8[/tex]

Degree is the highest power of the function. Since, the given function has degree 3. So, it is odd.

So, The graph will be in opposite direction.

Also, The leading coefficient is 1 (coefficient of highest degree) and positive so the left side of the graph continues down the coordinate plane and the right side continues upward.

Also, The graph shifts 8 units downward from the origin.

Thus, Option (a) is correct.

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.