Describe the end behavior (long run behavior) of $$ f(x)=-x^{8} $$ As $$ x \rightarrow-\infty, f(x) \rightarrow ? \vee $$ As $$ x \rightarrow \infty, f(x) \rightarrow ? $$

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To analyze the end behavior of the function $$ f(x) = -x^8 $$, we need to consider the behavior of the function as $$ x $$ approaches negative infinity and positive infinity.

1. **As $$ x \rightarrow -\infty $$**:
   - The term $$ x^8 $$ is raised to an even power, which means it will always be positive regardless of whether $$ x $$ is negative or positive. Therefore, as $$ x $$ becomes very large in the negative direction, $$ x^8 $$ will also become very large (but positive).
   - Since $$ f(x) = -x^8 $$, as $$ x $$ approaches negative infinity, $$ -x^8 $$ will approach negative infinity.
   - Thus, we have:
     $$
     \text{As } x \rightarrow -\infty, f(x) \rightarrow -\infty.
     $$

2. **As $$ x \rightarrow \infty $$**:
   - Again, since $$ x^8 $$ is positive for positive values of $$ x $$, as $$ x $$ approaches positive infinity, $$ x^8 $$ will also approach positive infinity.
   - Consequently, $$ f(x) = -x^8 $$ will approach negative infinity as well.
   - Thus, we have:
     $$
     \text{As } x \rightarrow \infty, f(x) \rightarrow -\infty.
     $$

In summary, the end behavior of the function $$ f(x) = -x^8 $$ is:
- As $$ x \rightarrow -\infty, f(x) \rightarrow -\infty $$.
- As $$ x \rightarrow \infty, f(x) \rightarrow -\infty $$.
- As $$ x \rightarrow -\infty, f(x) \rightarrow -\infty $$. - As $$ x \rightarrow \infty, f(x) \rightarrow -\infty $$.

Describe the end behavior (long run behavior) of
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As

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