End Behavior of Functions

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•
Mathematics
•
10th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the end behavior of a polynomial function?
Back
The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.
2.
FLASHCARD QUESTION
Front
How does the degree of a polynomial affect its end behavior?
Back
The degree of a polynomial determines the number of times the graph can turn and the direction in which it goes as x approaches infinity or negative infinity. Odd-degree polynomials have opposite end behaviors, while even-degree polynomials have the same end behavior.
3.
FLASHCARD QUESTION
Front
What is the leading coefficient test?
Back
The leading coefficient test helps determine the end behavior of a polynomial function based on the sign of the leading coefficient and the degree of the polynomial.
4.
FLASHCARD QUESTION
Front
For a polynomial of even degree with a positive leading coefficient, what is the end behavior?
Back
As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches +∞.
5.
FLASHCARD QUESTION
Front
For a polynomial of even degree with a negative leading coefficient, what is the end behavior?
Back
As x approaches -∞, f(x) approaches -∞; as x approaches +∞, f(x) approaches -∞.
6.
FLASHCARD QUESTION
Front
For a polynomial of odd degree with a positive leading coefficient, what is the end behavior?
Back
As x approaches -∞, f(x) approaches -∞; as x approaches +∞, f(x) approaches +∞.
7.
FLASHCARD QUESTION
Front
For a polynomial of odd degree with a negative leading coefficient, what is the end behavior?
Back
As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches -∞.
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