Question

consider the polynomial function $h(x) = -7x^6 + 3x^4 - 5x^2$. what is the end behavior of the graph of $h$?

Explanation:

Step1: Identify leading term

The leading term of $h(x)$ is $-7x^6$.

Step2: Analyze degree and sign

Degree (6) is even, leading coefficient (-7) is negative.

Step3: Define end behavior

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

Answer:

As $x$ approaches positive infinity, $h(x)$ approaches negative infinity; as $x$ approaches negative infinity, $h(x)$ approaches negative infinity.
Or concisely:
$\text{As } x\to\pm\infty,\ h(x)\to-\infty$