Question

describe the long run behavior of $f(x) = -x^7$
as $x \to -\infty$, $f(x) \to$ ?
as $x \to \infty$, $f(x) \to$ ?
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Explanation:

Step1: Analyze \(x \to -\infty\)

For \(f(x)=-x^{7}\), when \(x\to -\infty\), \(x^{7}\to -\infty\) (since odd power of negative number is negative). Then \(-x^{7}\to -(-\infty)=\infty\).

Step2: Analyze \(x \to \infty\)

When \(x\to \infty\), \(x^{7}\to \infty\) (odd power of positive number is positive). Then \(-x^{7}\to -\infty\).

Answer:

As \(x \to -\infty\), \(f(x) \to \infty\)
As \(x \to \infty\), \(f(x) \to -\infty\)