Question

(b) $g(x)=3x^{6}-7x^{5}-8x^{2}-9$ 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 and leading coefficient

Degree of $g(x)$ is 6 (even), leading coefficient is 3 (positive).

Step2: Apply end behavior rules

For even degree, positive leading coefficient: as $x\to-\infty$, $g(x)\to+\infty$; as $x\to+\infty$, $g(x)\to+\infty$. This means the graph rises on both left and right.

Answer:

Rises to the left and rises to the right