MAC 1140C Lecture Notes - Precalculus, Coefficient, Division Algorithm
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10 Oct 2022
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Polynomial functions: f(x)= anxn+an-1xn-1 the domain is all real numbers. If n is a positive even integer: f is an even function so its graph is symmetric to the y-axis, the domain is all real number and the range is all real nonnegative numbers. If n is a positive odd integer: f is an odd function so its graph is symmetric to the origin, the domain and range are a set of all real numbers. Zero of an even multiplicity: the graph touches the x-axis at the zero. Zero of an odd multiplicity: the graph crosses the x-axis at the zero. Turning points: degree minus 1 is the number of turning points of the graph n: degree an: leading coefficient. Descartes rule of signs: the number of positive real zeros of f either equals the number of variations in the sign of the nonzero coefficients of f(x) or else equals that number less an even integer.
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