Questions: Describe the long run behavior of f(p)=p^9-2p^6-3p^5+3 As p -> -∞, f(p) -> ? As p -> ∞, f(p) -> ?

Transcript text: Describe the long run behavior of $f(p)=p^{9}-2 p^{6}-3 p^{5}+3$ As $p \rightarrow-\infty, f(p) \rightarrow$ ? As $p \rightarrow \infty, f(p) \rightarrow$ ?

Solution

Solution Steps

Step 1: Identify the Leading Term

The leading term of the polynomial is $x^9$.

Step 2: Analyze the Leading Coefficient and Degree

Since the degree 9 is odd and the leading coefficient 1 is positive, as $x \rightarrow -\infty$, $f(x) \rightarrow -\infty$, and as $x \rightarrow \infty$, $f(x) \rightarrow \infty$.

Final Answer:

As $x \rightarrow -\infty$, the polynomial's behavior is towards $-\infty$, and as $x \rightarrow \infty$, it is towards $\infty$. Rounded to 0 decimal places.

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