Properties of Polynomial Functions
Loading the math board and drawing, please wait…
This example demonstrates the properties of polynomial function graphs and their variations. It involves core math concepts like functions, polynomial functions, reflection, algebra, real numbers, congruence, and quadratic functions. The construction uses GeoGebra commands such as If, objects like dummy, Degree, g, e, d, c, b, a, Leading_Coefficient, Number_Terms, f, text2, and text3. It is suitable for high school mathematics teaching to understand the characteristics and parameter effects of polynomial function graphs.
GeoGebra Commands & Parameters
If(Number_ Terms - 1 > Degree, x + 100, If[Number_ Terms ≟ 1, (Leading_ Coefficient * x^(Degree)), If[Number_ Terms ≟ 2, (Leading_ Coefficient * x^(Degree)) + (a * x^(Degree - 1)), If[Number_ Terms ≟ 3, (Leading_ Coefficient * x^(Degree)) + (a * x^(Degree - 1)) + (b * x^(Degree - 2)), If[Number_ Terms ≟ 4, (Leading_ Coefficient * x^(Degree)) + (a * x^(Degree - 1)) + (b * x^(Degree - 2)) + (c * x^(Degree - 3)), If[Number_ Terms ≟ 5, (Leading_ Coefficient * x^(Degree)) + (a * x^(Degree - 1)) + (b * x^(Degree - 2)) + (c * x^(Degree - 3)) + (d * x^(Degree - 4)), If[Number_ Terms ≟ 6, (Leading_ Coefficient * x^(Degree)) + (a * x^(Degree - 1)) + (b * x^(Degree - 2)) + (c * x^(Degree - 3)) + (d * x^(Degree - 4)) + (e * x^(Degree - 5)), If[Number_ Terms ≟ 7, (Leading_ Coefficient * x^(Degree)) + (a * x^(Degree - 1)) + (b * x^(Degree - 2)) + (c * x^(Degree - 3)) + (d * x^(Degree - 4)) + (e * x^(Degree - 5)) + (g * x^(Degree - 6)), x + 100]]]]]]]) → f