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

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The function is given by $$ f(x) = -x^8 $$.

1. Since the exponent $$ 8 $$ is even, $$ x^8 $$ is always non-negative for any real number $$ x $$.

2. As $$ |x| $$ increases, $$ x^8 $$ grows very large.

3. Because there is a negative sign in front ($$ -x^8 $$), the function will be very large in the negative sense for large $$ |x| $$.

Thus:

- As $$ x \rightarrow -\infty $$, $$ x^8 \rightarrow \infty $$ and hence $$ f(x) = -x^8 \rightarrow -\infty $$.
- As $$ x \rightarrow \infty $$, $$ x^8 \rightarrow \infty $$ and hence $$ f(x) = -x^8 \rightarrow -\infty $$.
As $$ x $$ approaches negative infinity, $$ f(x) $$ approaches negative infinity. As $$ x $$ approaches positive infinity, $$ f(x) $$ also approaches negative infinity.

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

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