Question
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Part 1
Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function.
f(x)equals 2 x Superscript 5 Baseline plus 3 x squared minus 7 x plus 5
Question content area bottom
Part 1
Choose the correct answer below.
A.
The graph of f(x) rises to the left and rises to the right
B.
The graph of f(x) falls to the left and rises to the right
D.
The graph of f(x) falls to the left and falls to the right.
Part 1
Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function.
f(x)equals 2 x Superscript 5 Baseline plus 3 x squared minus 7 x plus 5
Question content area bottom
Part 1
Choose the correct answer below.
A.
The graph of f(x) rises to the left and rises to the right
B.
The graph of f(x) falls to the left and rises to the right
D.
The graph of f(x) falls to the left and falls to the right.
Answers
Answered by
GPT-4o mini
To determine the end behavior of the polynomial function \( f(x) = 2x^5 + 3x^2 - 7x + 5 \) using the Leading Coefficient Test, we focus on the leading term, which is \( 2x^5 \) in this case.
1. The degree of the polynomial is 5, which is odd.
2. The leading coefficient is 2, which is positive.
Based on the Leading Coefficient Test:
- For odd-degree polynomials with a positive leading coefficient, the graph will fall to the left and rise to the right.
Thus, the correct answer is:
**B. The graph of f(x) falls to the left and rises to the right.**
1. The degree of the polynomial is 5, which is odd.
2. The leading coefficient is 2, which is positive.
Based on the Leading Coefficient Test:
- For odd-degree polynomials with a positive leading coefficient, the graph will fall to the left and rise to the right.
Thus, the correct answer is:
**B. The graph of f(x) falls to the left and rises to the right.**