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. The focus is on recognizing how the leading term and its coefficient determine the end behavior as .
Key Concept Explanation
For a polynomial function, the end behavior is determined by the degree and the sign of the leading coefficient. If the degree is odd and the leading coefficient is positive, the right end of the graph (as ) will go up.
Step-by-step Solution
1. Identify the degree of the polynomial: The degree is 5 (odd).
2. Identify the leading coefficient: The leading coefficient is 2 (positive).
3. Determine the end behavior: Since the degree is odd and the leading coefficient is positive, as
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