Questions: Use the leading coefficient test to determine the end behavior of the graph of the given polynomial function. f(x)=7x^7-5x^5+2x^4+2 A. Falls left rises right. B. Falls left falls right. C. Rises left rises right. D. Rises left falls right. E. None of the above.

Use the leading coefficient test to determine the end behavior of the graph of the given polynomial function.
f(x)=7x^7-5x^5+2x^4+2
A. Falls left rises right.
B. Falls left falls right.
C. Rises left rises right.
D. Rises left falls right.
E. None of the above.

Transcript text: (3.5) Use the leading coefficient test to determine the end behavior of the graph of the given polynomial function. \[ f(x)=7 x^{7}-5 x^{5}+2 x^{4}+2 \] A. Falls left \& rises right. B. Falls left \& falls right. C. Rises left \& rises right. D. Rises left \& falls right. E. None of the above.

Solution

Solution Steps

Step 1: Identify the Leading Term

The leading term of the polynomial is $7x^7$. This term determines the end behavior of the graph.

Step 2: Apply the Leading Coefficient Test

Since the leading term is $7x^7$, and considering the degree of the polynomial (n=7) and the leading coefficient (a_n=7), we apply the Leading Coefficient Test to determine the end behavior of the graph.

Step 3: Determine the End Behavior

Based on the leading coefficient and the degree of the polynomial, the graph falls to the left and rises to the right.

Final Answer:

The end behavior of the graph of the given polynomial function, based on its leading term $7x^7$, is that it falls to the left and rises to the right.

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