Example of Polynomial Function Addition, Subtraction, and Multiplication
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This example demonstrates how to find (f + g)(x), (f – g)(x), and (f • g)(x) given the polynomial functions f(x) = –2x^2 – 2x + 1 and g(x) = x + 1. The key mathematical concepts involved are the addition, subtraction, and multiplication of polynomial functions. Using GeoGebra commands such as If and Simplify, the graphs of these functions can be clearly constructed. Suitable for high school mathematics education.
GeoGebra Commands & Parameters
If(f(((-gc)) / gx) ≟ 0, If[f((gc + 1) / gx) ≟ 0, gc + 2, gc + 1], gc) → gc1Simplify((gx * x) + gc1) → gSimplify(f(x) + g(x)) → fplusgSimplify(f(x) - g(x)) → fminusgSimplify((f(x) * g(x))) → ftimesgSimplify(f(x) / g(x)) → fdividegSimplify((-g(x))) → gminusSimplify(((fx2 * gx) * x^(3))) → fg1Simplify(((fx * gx) * x^(2))) → fg2Simplify(((fx2 * gc1) * x^(2))) → fg4Simplify(((fx * gc1) * x)) → fg5Simplify((fc * gc)) → fg6Simplify(((fc * gx) * x)) → fg3
AI Drawing Prompt Reference
Plot the two given polynomial functions f(x) = -2x^2 - 2x + 1 and g(x) = x + 1, and then plot their sum, difference, product, and quotient. First, plot f(x) and g(x), then plot (f+g)(x), (f-g)(x), (f*g)(x), and (f/g)(x).
The prompt above was compiled from the original drawing commands and is for reference only.