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
C.
The graph of​ f(x) rises to the left and falls to the right.
D.
The graph of​ f(x) falls to the left and falls to the right.

Answer 1

To determine the end behavior of the polynomial function \( f(x) = 2x^5 + 3x^2 - 7x + 5 \) using the Leading Coefficient Test, we need to consider the leading term, which is the term with the highest degree.

1. **Degree of the polynomial**: The highest degree term is \( 2x^5 \), which means the degree is 5.
2. **Leading coefficient**: The leading coefficient (the coefficient of the highest degree term) is 2.

Now, we consider the following rules for end behavior:

- If the degree is **odd** (like 5), and the leading coefficient is **positive** (like 2), then:
- The graph will **rise** to the right and **fall** to the left.

Based on this analysis, the correct answer is:

**C. The graph of​ f(x) rises to the left and falls to the right.**