Which of the following describes the end behavior of the graph of a cubic function?

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Q: Which of the following describes the end behavior of the graph of a cubic function?

Solution: A cubic function has one end rising and the other falling, characteristic of odd-degree polynomials.

Steps: 4

Step 1: Understand what a cubic function is. A cubic function is a polynomial of degree 3, which means it has the form f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a is not zero.
Step 2: Identify the degree of the polynomial. Since a cubic function is of degree 3, it is classified as an odd-degree polynomial.
Step 3: Learn about the end behavior of odd-degree polynomials. For odd-degree polynomials, as x (the input) goes to positive infinity (very large positive numbers), the output (f(x)) also goes to positive infinity. Conversely, as x goes to negative infinity (very large negative numbers), the output goes to negative infinity.
Step 4: Conclude the end behavior of a cubic function. Therefore, the end behavior of a cubic function is that one end of the graph rises (goes up) while the other end falls (goes down).