Question

(b) $g(x)=4x^{4}+x^{3}+9x^{2}+3x$
falls to the left and rises to the right
rises to the left and falls to the right
rises to the left and rises to the right
falls to the left and falls to the right

Explanation:

Step1: Identify degree & leading coefficient

Degree of $g(x)$ is 4 (even), leading coefficient is 4 (positive).

Step2: Apply end behavior rules

For even degree, positive leading coefficient: as $x\to-\infty$, $g(x)\to+\infty$; as $x\to+\infty$, $g(x)\to+\infty$.

Answer:

Rises to the left and rises to the right