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Function and Inequality Verification Example

Function and Inequality Verification Example
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2015-11-03 04:25
FunctionCoordinate GeometryInequality
In collections CCSS Support Math II Unit 2
This example demonstrates how to verify whether the ordered pair (5, 19) satisfies the function g(x) = 5x – 6 and the inequality y > 5x – 6. The core mathematical concepts involved include function verification and inequality judgment. The construction highlights the use of GeoGebra commands and objects such as SelectedElement, LaTeX, SelectedIndex, If, and elements like Border, Gear, Book, etc. It is suitable for high school mathematics teaching and function graph analysis.

GeoGebra Commands & Parameters

  1. SelectedElement(FXC) → FXCV
  2. SelectedElement(FXX) → FXXV
  3. SelectedElement(GXC) → GXCV
  4. SelectedElement(GXX) → GXXV
  5. LaTeX("\text{Substitute the ordered pair into the function and simplify.}") → text2_2
  6. LaTeX("\text{Rewritten function}") → text2_5
  7. LaTeX("\text{Given inequality}") → text2_{17}
  8. LaTeX("\text{Rewrite the function \textcolor{#000099}{g(x) = 5x\; –\; 6} so that it is not in function notation.}") → text2
  9. LaTeX((((("{Does\; the\; ordered \;pair\; \textcolor{#000099}{(" * FXXV) * "}, \textcolor{#000099}{") * FXCV) * ")}\; satisfy \;the \;function\; \textcolor{#000099}{g(x) = 5x \;–\; 6?}\; Does\; it\; satisfy \;the\; inequality\; \textcolor{#000099}{ y > 5x\; –\; 6?}}")) → text1
  10. LaTeX((((("\text{\textcolor{#000099}{" * FXCV) * " = ") * valu1) * "\;–\; 6}")) → text2_8
  11. LaTeX((((("\text{\textcolor{#000099}{" * FXCV) * " = ") * valu2) * "}}")) → text2_9
  12. LaTeX((("\text{Multiply \textcolor{#000099}{5} by \textcolor{#000099}{" * FXXV) * "}.}")) → text2_{11}
  13. LaTeX((("\text{Subtract \textcolor{#000099}{6} from \textcolor{#000099}{" * valu1) * "}.}")) → text2_{10}
  14. LaTeX((("\text{Multiply \textcolor{#000099}{5} by \textcolor{#000099}{" * FXXV) * "}.}")) → text2_{21}
  15. LaTeX((("\text{Subtract \textcolor{#000099}{6} from \textcolor{#000099}{" * valu1) * "}.}")) → text2_{23}
  16. LaTeX("\text{Substitute the ordered pair into the inequality \textcolor{#000099}{y > 5x\; –\; 6} and simplify.}") → text2_{14}
  17. LaTeX((((("\text{\textcolor{#000099}{" * FXCV) * " > ") * valu1) * "\;–\; 6}")) → text2_{20}
  18. LaTeX((((("\text{\textcolor{#000099}{" * FXCV) * " > ") * valu2) * "}}")) → text2_{22}
  19. SelectedIndex(FXX_1) → FXXV_1
  20. SelectedIndex(FXC_1) → FXCV_1
  21. SelectedIndex(FXX_2) → FXXV_2
  22. LaTeX((((("\text{statement, the ordered pair \textcolor{#000099}{(" * FXXV_2) * "},\textcolor{#000099}{") * FXCV_1) * ")} not satisfies the function \textcolor{#000099}{g(x) = 5x \;–\; 6}.}")) → text2_{27}
  23. LaTeX((((("\text{Once simplified, the equation is \textcolor{#000099}{" * FXCV_1) * " = ") * valu2_2) * "}. Because this is a false}")) → text2_{26}
  24. LaTeX("\text{one element of the range; that is, for every value of x, there is exactly }") → text3_1
  25. LaTeX("\text{one value of y. }") → text3_2
  26. LaTeX("\text{quantities that are not equivalent}") → text3_3
  27. If(FXCV ≠ valu2, LaTeX[(((("\text{Once simplified, the equation is \textcolor{#000099}{" * FXCV) * " = ") * valu2) * "}. Because this is a false}")], LaTeX[(((("\text{Once simplified, the equation is \textcolor{#000099}{" * FXCV) * " = ") * valu2) * "}. Because this is a true}")]) → text2_{12}
  28. If(FXCV ≥ valu2, LaTeX[(((("\text{Once simplified, the inequality is \textcolor{#000099}{" * FXCV) * " > ") * valu2) * "}. Because this is not a true statement,}")], LaTeX[(((("\text{Once simplified, the inequality is \textcolor{#000099}{" * FXCV) * " > ") * valu2) * "}. Because this is a true statement,}")]) → text2_{24}
  29. LaTeX((((("\text{\textcolor{#000099}{(" * FXCV) * ")}=\textcolor{#000099}{5}\textcolor{#000099}{(") * FXXV) * ")} \textcolor{#000099}{- 6}}")) → text2_6
  30. LaTeX((((("\text{\textcolor{#000099}{(" * FXCV) * ")}\textcolor{#000099}{>5}\textcolor{#000099}{(") * FXXV) * ")} \textcolor{#000099}{- 6}}")) → text2_{18}
  31. LaTeX((((((((("\text{The ordered pair is \textcolor{#000099}{(" * FXXV) * "},\textcolor{#000099}{") * FXCV) * ")}. Substitute \textcolor{#000099}{") * FXXV) * "} for \textcolor{#000099}{x} and \textcolor{#000099}{") * FXCV) * "} for \textcolor{#000099}{y}.}")) → text2_3
  32. LaTeX("\text{ \textcolor{#000099}{y = 5x\; –\; 6}}") → text2_4
  33. LaTeX((((("\text{Substitute \textcolor{#000099}{" * FXXV) * "} for \textcolor{#000099}{x} and \textcolor{#000099}{") * FXCV) * "} for \textcolor{#000099}{y}.}")) → text2_7
  34. LaTeX((((((((("\text{Use the same ordered pair, \textcolor{#000099}{(" * FXXV) * "},\textcolor{#000099}{") * FXCV) * ")}. Again, substitute \textcolor{#000099}{") * FXXV) * "} for \textcolor{#000099}{x} and \textcolor{#000099}{") * FXCV) * "} for \textcolor{#000099}{y}.}")) → text2_{15}
  35. LaTeX("\text{ \textcolor{#000099}{y > 5x\; –\; 6}}") → text2_{16}
  36. LaTeX((((("\text{Substitute \textcolor{#000099}{" * FXXV) * "} for \textcolor{#000099}{x} and \textcolor{#000099}{") * FXCV) * "} for \textcolor{#000099}{y}.}")) → text2_{19}
  37. LaTeX("\text{\mathbf{function} a relation in which every element of the domain is paired with exactly}") → text3
  38. LaTeX("\text{\mathbf{inequality} a mathematical sentence that shows the relationship between }") → text3_4
  39. LaTeX("\text{x-coordinate:}") → DKT1
  40. LaTeX("\text{y-coordinate:}") → DKT2
  41. If(FXCV ≥ valu2, LaTeX[(((("\text{the ordered pair \textcolor{#000099}{(" * FXXV) * "},\textcolor{#000099}{") * FXCV) * ")} does not satisfy the inequality \textcolor{#000099}{y > 5x\; –\; 6}.}")], LaTeX[(((("\text{the ordered pair \textcolor{#000099}{(" * FXXV) * "}, \textcolor{#000099}{") * FXCV) * ")} satisfies the inequality \textcolor{#000099}{y > 5x\; –\; 6}.}")]) → text2_{25}
  42. If(FXCV ≠ valu2, LaTeX[(((("\text{statement, the ordered pair \textcolor{#000099}{(" * FXXV) * "},\textcolor{#000099}{") * FXCV) * ")} does not satisfy the function \textcolor{#000099}{g(x) = 5x \;–\; 6}.}")], LaTeX[(((("\text{statement, the ordered pair \textcolor{#000099}{(" * FXXV) * "},\textcolor{#000099}{") * FXCV) * ")} satisfies the function \textcolor{#000099}{g(x) = 5x \;–\; 6}.}")]) → text2_{13}
  43. LaTeX("\text{To rewrite the function \textcolor{#000099}{g(x) = 5x\; –\; 6} so that it is not in function notation, replace \textcolor{#000099}{g(x)} with \textcolor{#000099}{y} to get \textcolor{#000099}{y = 5x\; –\; 6}.}") → text2_1