Examine the polynomial function . As , , and as , .
Answer & Analysis
Analysis
Question Analysis
This question assesses the student's ability to determine the end behavior of a polynomial function with an odd degree and a positive leading coefficient, considering both positive and negative infinity.
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 polynomial with a positive leading coefficient, as , the function values go to , and as , the function values go to .
Step-by-step Solution
1. Identify the degree of the polynomial: The degree is 7 (odd).
2. Identify the leading coefficient: The leading coefficient is 7 (positive).
3. Apply the end behavior rule for odd-degree polynomials with a positive leading coefficient: As ,
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