Polynomials - End Behavior and Graphs

Flashcard
•
Mathematics
•
11th - 12th Grade
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a polynomial?
Back
A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 3x^2 + 2x + 1 is a polynomial.
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. For example, in the polynomial 4x^3 + 2x^2 + 5, the degree is 3.
3.
FLASHCARD QUESTION
Front
How does the end behavior of a polynomial function relate to its degree?
Back
The end behavior of a polynomial function is determined by its leading term. If the degree is even, both ends of the graph will go in the same direction. If the degree is odd, the ends will go in opposite directions.
4.
FLASHCARD QUESTION
Front
What is the leading coefficient of a polynomial?
Back
The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x^4 + 3x^2 + 2, the leading coefficient is 5.
5.
FLASHCARD QUESTION
Front
Describe the end behavior of a polynomial function with a positive leading coefficient and an even degree.
Back
As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches +∞.
6.
FLASHCARD QUESTION
Front
Describe the end behavior of a polynomial function with a negative leading coefficient and an even degree.
Back
As x approaches -∞, f(x) approaches -∞; as x approaches +∞, f(x) approaches -∞.
7.
FLASHCARD QUESTION
Front
Describe the end behavior of a polynomial function with a positive leading coefficient and an odd degree.
Back
As x approaches -∞, f(x) approaches -∞; as x approaches +∞, f(x) approaches +∞.
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