Question

question 10 of 10
which of the following correctly describes the end behavior of the polynomial
function, $f(x) = 2x^4 - 3x^2 + 2x$?

a. the left end goes down and the right end goes up.

b. both ends go up.

c. both ends go down.

d. the left end goes up and the right end goes down.

Explanation:

Step1: Identify leading term

Leading term is $2x^4$ (highest degree term).

Step2: Analyze degree and coefficient

Degree is 4 (even), leading coefficient is 2 (positive).

Step3: Determine end behavior

For even degree + positive coefficient: as $x\to\pm\infty$, $f(x)\to\infty$.

Answer:

B. Both ends go up.