Question

What is the end behavior of (m) = (n = 3) (2 + 5) (9— 2)?

A. It rises to the left and rises to the right.
B. It rises to the left and falls to the right.
C. It falls to the left and rises to the right.
D. It falls to the left and falls to the right.

Answer 1

The end behavior of the function
`\( m(n) = (n - 3)(2n + 5)(9 - 2n) \)` is described as falling to the left and rising to the right. (Option C)

Step-by-step explanation:

To determine the end behavior of the polynomial function, we look at the leading term, which is the term with the highest degree. In this case, the leading term is
`\( (n - 3)(2n + 5)(-2n + 9) \)`. When we expand and simplify this expression, we get a cubic polynomial in the form
`\( an^3 + bn^2 + cn + d \)`, where
`\( a, b, c, \)` and
`\( d \)` are constants.

The leading term
`\( an^3 \)` indicates the degree and the leading coefficient. In our case, since the leading term has an odd degree (3), and the leading coefficient
`\( a \)` is negative, the end behavior is described as falling to the left and rising to the right.

Understanding end behavior is crucial for understanding the long-term trends of a function. In this context, as
`\( n \)` approaches negative or positive infinity, the function approaches negative infinity to the left and positive infinity to the right.

It's important to note that this analysis is based on the behavior of the leading term and the general shape of the polynomial. Further calculations, such as finding roots or critical points, can provide more insights into the overall behavior of the function.(Option C)