Questions: Describe the end behavior of the graph of the polynomial function. f(x)=9x^8-4x^4+x^2-5

Solution Steps

The leading term of the polynomial $f(x) = 9x^6 - 4x^4 + x^2 - 5$ is $9x^6$.

The leading term has a positive coefficient (9) and an even degree (6).

Since the leading coefficient is positive and the degree is even, the end behavior of the graph is as follows:

• As $x$ approaches negative infinity ($x \to -\infty$), $f(x)$ approaches positive infinity ($f(x) \to \infty$).
• As $x$ approaches positive infinity ($x \to \infty$), $f(x)$ approaches positive infinity ($f(x) \to \infty$).

Final Answer: A