End Behavior & Zeros of Polynomials
Flashcard
•
Mathematics
•
11th Grade
•
Hard
Standards-aligned
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15 questions
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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.
2.
FLASHCARD QUESTION
Front
How do you determine the end behavior of a polynomial function?
Back
To determine the end behavior, look at the leading term of the polynomial. The sign and degree of the leading term dictate the behavior as x approaches ±∞.
3.
FLASHCARD QUESTION
Front
What does it mean if a polynomial has an odd degree and a negative leading coefficient?
Back
If a polynomial has an odd degree and a negative leading coefficient, as x → ∞, f(x) → -∞ and as x → -∞, f(x) → ∞.
4.
FLASHCARD QUESTION
Front
What does it mean if a polynomial has an even degree and a positive leading coefficient?
Back
If a polynomial has an even degree and a positive leading coefficient, as x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞.
5.
FLASHCARD QUESTION
Front
What are the zeros of a polynomial function?
Back
The zeros of a polynomial function are the values of x for which the function equals zero. They are the x-intercepts of the graph.
Tags
CCSS.HSF-IF.C.7C
6.
FLASHCARD QUESTION
Front
How do you find the zeros of the polynomial y = x(x - 6)(x + 5)?
Back
Set the polynomial equal to zero: x(x - 6)(x + 5) = 0. The zeros are x = 0, x = 6, and x = -5.
Tags
CCSS.HSF-IF.C.7C
7.
FLASHCARD QUESTION
Front
What is the significance of the leading coefficient in determining end behavior?
Back
The leading coefficient determines the direction of the graph as x approaches ±∞. A positive leading coefficient means the graph rises to the right, while a negative one means it falls.
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