Analyze the end behavior of the polynomial function . As , , and as , .
Answer & Analysis
Analysis
Question Analysis
This question evaluates the student's understanding of the end behavior of a polynomial function, particularly for polynomials with odd degrees.
Key Concept Explanation
The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient. For an odd degree with a positive leading coefficient, the left end goes down and the right end goes up.
Step-by-step Solution
1. Identify the degree of the polynomial: 9 (odd).
2. Identify the leading coefficient: 2 (positive).
3. Since the degree is odd and the leading coefficient is positive, the left end goes down and the right end goes up.
4. Therefore, as , , and as
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