Polynomial Functions
Flashcard
•
Mathematics
•
9th - 11th Grade
•
Practice Problem
•
Hard
+2
Standards-aligned
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14 questions
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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. For example, in P(x) = 3x^4 - 7x^2 + 2, the degree is 4.
3.
FLASHCARD QUESTION
Front
What does it mean for a polynomial to be even?
Back
A polynomial is even if f(-x) = f(x) for all x in its domain. This means the graph of the polynomial is symmetric with respect to the y-axis.
Tags
CCSS.HSF.BF.B.3
4.
FLASHCARD QUESTION
Front
What does it mean for a polynomial to be odd?
Back
A polynomial is odd if f(-x) = -f(x) for all x in its domain. This means the graph of the polynomial is symmetric with respect to the origin.
5.
FLASHCARD QUESTION
Front
How do you evaluate a polynomial function at a specific value?
Back
To evaluate a polynomial function at a specific value, substitute the value into the polynomial expression and simplify. For example, for f(x) = 3x^2 - 9x - 20, to find f(5), substitute 5 for x.
Tags
CCSS.HSF.IF.A.2
6.
FLASHCARD QUESTION
Front
What is a leading coefficient?
Back
The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It determines the end behavior of the polynomial's graph.
7.
FLASHCARD QUESTION
Front
What is the significance of the leading coefficient's sign?
Back
The sign of the leading coefficient affects the direction of the graph's ends: if positive, the graph rises to the right; if negative, it falls to the right.
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