HAA Zeros and End Behavior

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What are the zeros of the function f(x) = (x+2)(x-3)²(x-4)?
Back
The zeros are -2, 3 (multiplicity 2), and 4.
Tags
CCSS.HSF-IF.C.7C
2.
FLASHCARD QUESTION
Front
What does the term 'multiplicity' mean in relation to polynomial zeros?
Back
Multiplicity refers to the number of times a particular zero appears as a root of the polynomial. For example, if a zero has a multiplicity of 2, it means that the factor corresponding to that zero is squared.
Tags
CCSS.HSF-IF.C.7C
3.
FLASHCARD QUESTION
Front
According to the Fundamental Theorem of Algebra, how many zeros does a polynomial function of degree n have?
Back
A polynomial function of degree n has exactly n zeros, counting multiplicities.
Tags
CCSS.HSN.CN.C.9
4.
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.
5.
FLASHCARD QUESTION
Front
How do you determine the end behavior of the function f(x) = - (x² - 9)(x + 4)?
Back
Since the leading coefficient is negative and the degree is odd, as x approaches positive infinity, f(x) approaches negative infinity, and as x approaches negative infinity, f(x) approaches positive infinity.
6.
FLASHCARD QUESTION
Front
What is the significance of the leading coefficient in a polynomial function?
Back
The leading coefficient determines the direction of the end behavior of the polynomial function. If it is positive, the ends of the graph will rise in both directions; if negative, the ends will fall.
7.
FLASHCARD QUESTION
Front
What are the zeros of the function f(x) = -7x(x-5)³(x+6)?
Back
The zeros are x = 0, x = 5 (multiplicity 3), and x = -6.
Tags
CCSS.HSF-IF.C.7C
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