Question

consider the polynomial function $q(x) = 3x^4 - 5x^3 - 2x^2 + x - 18$. what is the end behavior of the graph of $q$?

Explanation:

Step1: Identify leading term

The leading term of $q(x)$ is $3x^4$.

Step2: Analyze degree and leading coefficient

Degree (4) is even; leading coefficient (3) is positive.

Step3: Define end behavior rules

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

Answer:

As $x$ approaches positive infinity ($x\to\infty$), $q(x)$ approaches positive infinity ($q(x)\to\infty$); as $x$ approaches negative infinity ($x\to-\infty$), $q(x)$ approaches positive infinity ($q(x)\to\infty$).