Question

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

(f(x) = 5x^4 + 3x^2 - x + 4)

choose the correct answer below.

a. the graph of (f(x)) falls to the left and rises to the right.
b. the graph of (f(x)) rises to the left and rises to the right.
c. the graph of (f(x)) falls to the left and falls to the right.
d. the graph of (f(x)) rises to the left and falls to the right.

Explanation:

Identify the leading term

Using the Leading Coefficient Test and Degree of Polynomial knowledge points

$$
LATEXBLOCK0
$$

Determine degree and leading coefficient

Using the Degree of Polynomial and Leading Coefficient Test knowledge points

$$
LATEXBLOCK1
$$

Apply the Leading Coefficient Test

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

$$
LATEXBLOCK2
$$

Answer:

• A. The graph of f(x) falls to the left and rises to the right
• B. The graph of f(x) rises to the left and rises to the right (Correct answer)
• C. The graph of f(x) falls to the left and falls to the right
• D. The graph of f(x) rises to the left and falls to the right