Questions: Falls to the left and rises to the right Rises to the left and falls to the right Rises to the left and rises to the right Falls to the left and falls to the right

Solution Steps

The given text appears to describe the end behavior of polynomial functions. To determine the end behavior of a polynomial function, we need to look at the leading term, which is the term with the highest degree. The coefficient and the degree of this term will tell us how the function behaves as \( x \) approaches positive and negative infinity.

1. Falls to the left and rises to the right: This describes a polynomial with an odd degree and a positive leading coefficient.
2. Rises to the left and falls to the right: This describes a polynomial with an odd degree and a negative leading coefficient.
3. Rises to the left and rises to the right: This describes a polynomial with an even degree and a positive leading coefficient.
4. Falls to the left and falls to the right: This describes a polynomial with an even degree and a negative leading coefficient.

Let's write Python code to determine the end behavior of a polynomial given its leading term.

Given the polynomial's leading term, we have:

• Degree: \(3\)
• Coefficient: \(2\)

For a polynomial function, the end behavior is determined by the degree and the leading coefficient:

• If the degree is odd and the leading coefficient is positive, the polynomial falls to the left and rises to the right.

Final Answer