APPC Polynomial Review

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What is an even function?

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A function f(x) is even if f(-x) = f(x) for all x in the domain of f. The graph of an even function is symmetric about the y-axis.

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What is an odd function?

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A function f(x) is odd if f(-x) = -f(x) for all x in the domain of f. The graph of an odd function is symmetric about the origin.

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What does it mean for a function to be neither even nor odd?

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A function is neither even nor odd if it does not satisfy the conditions for being even or odd. This means that f(-x) is not equal to f(x) or -f(x) for all x.

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What is the end behavior of a polynomial function?

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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.

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What is the significance of the leading coefficient in a polynomial?

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The leading coefficient determines the direction of the end behavior of the polynomial. If it is positive, the function will rise to infinity as x approaches infinity for odd-degree polynomials.

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What does it mean for a polynomial to be decreasing on an interval?

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A polynomial is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) > f(x2).

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The function is negative on the interval (-∞, -4) U (-1, 2).

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What is the definition of a polynomial function?

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable x in the polynomial expression.