Polynomial Functions

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What is a polynomial function?

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A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is: f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

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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 in the polynomial expression. For example, in f(x) = 2x^3 + 3x^2 + 1, the degree is 3.

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What does it mean for a polynomial to be even?

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A polynomial is even if f(-x) = f(x) for all x in its domain. This means the graph is symmetric with respect to the y-axis.

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What does it mean for a polynomial to be odd?

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A polynomial is odd if f(-x) = -f(x) for all x in its domain. This means the graph is symmetric with respect to the origin.

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How do you find the y-intercept of a polynomial function?

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The y-intercept of a polynomial function is found by evaluating the function at x = 0. For example, for f(x) = 2x^2 + 3x - 5, the y-intercept is f(0) = -5.

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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.

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What is a leading coefficient?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in f(x) = 4x^5 + 2x^3, the leading coefficient is 4.

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What is the significance of the degree of a polynomial?

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The degree of a polynomial determines the number of roots (solutions) it can have, the shape of its graph, and its end behavior.

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How do you determine if a polynomial function is increasing or decreasing?

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A polynomial function is increasing where its derivative is positive and decreasing where its derivative is negative.

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What is a root of a polynomial function?

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A root of a polynomial function is a value of x for which f(x) = 0. Roots can be real or complex.