Question

which describes the end behavior of the graph of the function $f(x) = -8x^4 - 2x^3 + x$?
(1 point)

• $f(x) \to \infty$ as $x \to -\infty$ and $f(x) \to \infty$ as $x \to \infty$
• $f(x) \to -\infty$ as $x \to -\infty$ and $f(x) \to -\infty$ as $x \to \infty$
• $f(x) \to \infty$ as $x \to -\infty$ and $f(x) \to -\infty$ as $x \to \infty$
• $f(x) \to -\infty$ as $x \to -\infty$ and $f(x) \to \infty$ as $x \to \infty$

Explanation:

Step1: Identify leading term

The leading term is $-8x^4$.

Step2: Analyze degree and sign

Degree (4) is even, leading coefficient (-8) is negative.

Step3: Determine end behavior

For even degree, $x
ightarrow\pm\infty$ makes $x^4
ightarrow\infty$. Multiply by $-8$: $-8x^4
ightarrow-\infty$. So $f(x)
ightarrow-\infty$ as $x
ightarrow-\infty$ and $x
ightarrow\infty$.

Answer:

$\boldsymbol{f(x)
ightarrow -\infty}$ as $\boldsymbol{x
ightarrow -\infty}$ and $\boldsymbol{f(x)
ightarrow -\infty}$ as $\boldsymbol{x
ightarrow \infty}$