Determine the end behavior of the polynomial function. As ,.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's understanding of the end behavior of a polynomial function based on its degree and leading coefficient.
Key Concept Explanation
The end behavior of a polynomial function is determined by the term with the highest degree (the leading term). For even-degree polynomials, if the leading coefficient is positive, both ends of the graph go up. If the leading coefficient is negative, both ends go down.
Step-by-step Solution
1. Identify the degree of the polynomial: The degree is 6 (even).
2. Identify the leading coefficient: The leading coefficient is 3 (positive).
3. Determine the end behavior: Since the degree is even and the leading coefficient is positive, as ,
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