Polynomial function graph

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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 f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.

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What determines the end behavior of a polynomial function?

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The end behavior of a polynomial function is determined by the leading coefficient and the degree of the polynomial.

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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.

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What does the leading coefficient indicate?

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The leading coefficient indicates the direction of the graph as x approaches positive or negative infinity, affecting the end behavior.

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What is a root of a polynomial?

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A root of a polynomial is a value of x for which the polynomial equals zero.

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What is multiplicity in relation to polynomial roots?

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Multiplicity refers to the number of times a particular root appears in a polynomial. A root with an even multiplicity touches the x-axis, while a root with an odd multiplicity crosses it.

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How do you find the x-intercepts of a polynomial function?

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To find the x-intercepts, set the polynomial equal to zero and solve for x.

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What is the factored form of a polynomial?

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The factored form of a polynomial expresses it as a product of its linear factors, which can reveal its roots.

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What is the significance of the y-intercept in polynomial functions?

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The y-intercept is the point where the graph of the polynomial crosses the y-axis, found by evaluating the polynomial at x=0.

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How can you determine the minimum degree of a polynomial function?

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The minimum degree of a polynomial function can be determined by the number of distinct roots and their multiplicities.