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Check if Point Satisfies Function and Inequality

Check if Point Satisfies Function and Inequality
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2015-10-13 23:50
FunctionCoordinate GeometryInequality
In collections CCSS Support Algebra I Unit 1 CCSS Support Math I Unit 1
This example demonstrates how to verify if the ordered pair (3,23) satisfies the function g(x)=7x+2 and the inequality y>7x+2. It involves core math concepts like functions, inequalities, and coordinate point validation. Construction highlights include using commands like SelectedElement, LaTeX, SelectedIndex, If, along with objects such as Border, Slider, and text2 for conditional judgment and visual representation. Suitable for middle school and above, aiding in teaching function and inequality properties.

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