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Function Addition Example

Function Addition Example
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2015-09-25 23:36
FunctionCoordinate GeometrySlider Animation
In collections CCSS Support Math II Unit 2
This example demonstrates how to construct a new function h(x) = (f + g)(x) given the linear functions f(x) = 4x + 1 and g(x) = 3x - 6. The key mathematical concept involved is function addition. The construction summary mentions the use of Border, Gear, Book, etc. It is suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. SelectedElement(FXC) → FXCV
  2. SelectedElement(FXX) → FXXV
  3. SelectedElement(GXC) → GXCV
  4. SelectedElement(GXX) → GXXV
  5. LaTeX("\text{Constant of f(x):}") → DKT2
  6. LaTeX("\text{Constant of g(x):}") → DKT4
  7. LaTeX("\text{Add the two functions.}") → PG1B
  8. LaTeX("\text{\textcolor{#000099}{h(x) = (f + g)(x) = f(x) + g(x)}}") → Pg1C
  9. LaTeX("\text{Combine like terms.}") → PG2A
  10. LaTeX("\text{Clear the parentheses and reorder the expression, then combine like terms.}") → PG2B
  11. LaTeX((((((((("\text{\textcolor{#000099}{h(x) = (" * FXXV) * "x + ") * FXCV) * ") + (") * GXXV) * "x ") * GXCV) * ")}}")) → Pg2C
  12. LaTeX("\text{Equation for \textcolor{#000099}{h(x)}}") → Pg2D
  13. LaTeX((((((((("\text{\textcolor{#000099}{h(x) = " * FXXV) * "x + ") * FXCV) * " + ") * GXXV) * "x ") * GXCV) * "}}")) → text1
  14. LaTeX("\text{Remove the parentheses.}") → Pg2F
  15. LaTeX("\text{Rearrange to group like terms.}") → Pg2H
  16. LaTeX((((((((("\text{\textcolor{#000099}{h(x) = " * FXXV) * "x + ") * GXXV) * "x + ") * FXCV) * " ") * GXCV) * "}}")) → Pg2G
  17. LaTeX((((("\text{\textcolor{#000099}{h(x) = " * ADDX) * "x ") * MinusX) * "}}")) → Pg2I
  18. LaTeX("\text{Combine like terms.}") → PG2J
  19. LaTeX("\text{where \textcolor{#000099}{a ≠ 0}. The graph of any quadratic function is a parabola.}") → WTK2
  20. LaTeX((((((((("\text{Given \textcolor{#000099}{f(x) = " * FXXV) * "x + ") * FXCV) * "} and \textcolor{#000099}{g(x) = ") * GXXV) * "x ") * GXCV) * "}, build a new function \textcolor{#000099}{h(x)}, for which \textcolor{#000099}{h(x) = (f + g)(x)}.}")) → Pg1A
  21. LaTeX((((((((((((((((("\text{Because \textcolor{#000099}{f(x) = " * FXXV) * "x + ") * FXCV) * "} and \textcolor{#000099}{g(x) = ") * GXXV) * "x ") * GXCV) * "}, adding \textcolor{#000099}{f(x)} and \textcolor{#000099}{g(x)} results in \textcolor{#000099}{h(x) = (f + g)(x) = (") * FXXV) * "x + ") * FXCV) * ") + (") * GXXV) * "x ") * GXCV) * ")}.}")) → PG1D
  22. LaTeX((((((((((((("\text{The result of adding \textcolor{#000099}{f(x) = " * FXXV) * "x + ") * FXCV) * "} and \textcolor{#000099}{g(x) = ") * GXXV) * "x ") * GXCV) * "} is \textcolor{#000099}{h(x) = ") * ADDX) * "x ") * MinusX) * "}.}")) → text2
  23. LaTeX("\text{\mathbf{quadratic\;function} a function that can be written in the form \textcolor{#000099}{f(x) = ax^2 + bx + c},}") → WTK1
  24. LaTeX("\text{x-value of f(x):}") → DKT1
  25. LaTeX("\text{x-value of g(x):}") → DKT3