5.3 Polynomial Functions and End Behavior

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Mathematics
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9th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a polynomial function?
Back
A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is P(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.
2.
FLASHCARD QUESTION
Front
What is the degree of a polynomial?
Back
The degree of a polynomial is the highest power of the variable in the polynomial expression. It determines the polynomial's end behavior and the number of roots.
3.
FLASHCARD QUESTION
Front
How do you determine the leading term of a polynomial?
Back
The leading term of a polynomial is the term with the highest degree. It is found by identifying the term with the largest exponent in the polynomial.
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.
5.
FLASHCARD QUESTION
Front
What does it mean if a polynomial has an even degree?
Back
If a polynomial has an even degree, its end behavior will be the same in both directions: as x approaches ±∞, f(x) approaches ±∞.
6.
FLASHCARD QUESTION
Front
What does it mean if a polynomial has an odd degree?
Back
If a polynomial has an odd degree, its end behavior will be opposite in each direction: as x approaches -∞, f(x) approaches -∞, and as x approaches +∞, f(x) approaches +∞.
7.
FLASHCARD QUESTION
Front
What is the significance of the leading coefficient?
Back
The leading coefficient of a polynomial affects the direction of the end behavior. If it is positive, the polynomial rises to the right; if negative, it falls to the right.
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