Examine the end behavior of the polynomial function . As , , and as , .
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to determine the end behavior of a polynomial function with an odd degree and a negative leading coefficient.
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 negative leading coefficient, the left end goes up and the right end goes down.
Step-by-step Solution
1. Identify the degree of the polynomial: 7 (odd).
2. Identify the leading coefficient: -3 (negative).
3. Since the degree is odd and the leading coefficient is negative, the left end goes up and the right end goes down.
4. Therefore, as ,
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