Question

use the leading coefficient test to determine the end behavior of the polynomial function.

(f(x) = -6x^3(x + 3)(x + 4)^2)

a. rises to the left and falls to the right
b. rises to the left and rises to the right
c. falls to the left and falls to the right
d. falls to the left and rises to the right

Explanation:

Identify the leading term of the polynomial

Using the Degree of Polynomial knowledge point

$$
LATEXBLOCK0
$$

Determine degree and leading coefficient

Using the Leading Coefficient Test and End Behavior of Polynomials knowledge points

$$
LATEXBLOCK1
$$

Apply the test for even degree and negative leading coefficient

Using the End Behavior of Polynomials knowledge point

$$
LATEXBLOCK2
$$

Answer:

• A. rises to the left and falls to the right
• B. rises to the left and rises to the right
• C. falls to the left and falls to the right (Correct answer)
• D. falls to the left and rises to the right