Question
Use the leading coefficient test to determine the end behavior of the graph of the given polynomial function.
A. Falls left
B. Falls left
C. Rises left
D. Rises left
E. None of the above.
A. Falls left
B. Falls left
C. Rises left
D. Rises left
E. None of the above.
Ask by Campos Huang. in the United States
Nov 02,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The end behavior is falls left and rises right.
Solution
To determine the end behavior of the polynomial function
-
Degree of the polynomial: The highest power of
in the polynomial is , which means the degree is . -
Leading coefficient: The leading coefficient is the coefficient of the term with the highest degree, which in this case is
.
Now, we can analyze the end behavior based on the degree and the leading coefficient:
-
Since the degree
is odd, the end behavior will be: - As
(left side), will go to . - As
(right side), will go to .
- As
-
The leading coefficient
is positive, which confirms that the function rises to the right.
Putting this together, we find that the end behavior of the graph of the polynomial function is:
- Falls left (as
) - Rises right (as
)
Thus, the correct answer is:
A. Falls left & rises right.
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Simplify this solution Mind Expander
To determine the end behavior of the polynomial function
Additionally, the degree of a polynomial not only influences its end behavior but also reveals information about the number of turning points. An odd-degree polynomial can have a maximum of
