Question

for the polynomial function f(x) = -2x⁴ - 6x³, answer the parts a through e.
a. use the leading coefficient test to determine the graph’s end behavior.
a. the graph of f(x) rises to the left and falls to the right.
b. the graph of f(x) falls to the left and falls to the right.
c. the graph of f(x) falls to the left and rises to the right.
d. the graph of f(x) rises to the left and rises to the right.

Explanation:

Step1: Identify Degree and Leading Coefficient

The polynomial \( f(x) = -2x^4 - 6x^3 \) has a degree of 4 (even) and a leading coefficient of -2 (negative).

Step2: Apply Leading Coefficient Test

For even degree polynomials:

• If leading coefficient is positive: graph rises to both left and right.
• If leading coefficient is negative: graph falls to both left and right.

Since degree is even (4) and leading coefficient is negative (-2), the graph falls to the left and falls to the right.

Answer:

B. The graph of \( f(x) \) falls to the left and falls to the right.