检验点是否满足函数与不等式

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2015-10-13 23:50

函数解析几何不等式

所属专题 CCSS Support Algebra I Unit 1 CCSS Support Math I Unit 1

①本范例演示如何检验有序对(3,23)是否满足函数g(x)=7x+2及不等式y>7x+2；②涉及核心数学概念：函数、不等式、坐标点验证；③构造要点：使用SelectedElement, LaTeX, SelectedIndex, If命令，结合Border, Slider, text2等对象进行条件判断与可视化展示；④适合初中及以上学生，用于函数与不等式性质的教学与理解。

GeoGebra 命令及参数

SelectedElement(FXC) → FXCV
SelectedElement(FXX) → FXXV
SelectedElement(GXC) → GXCV
SelectedElement(GXX) → GXXV
LaTeX("\text{Substitute the ordered pair into the function and simplify.}") → text2_2
LaTeX("\text{Rewritten function}") → text2_5
LaTeX("\text{Given inequality}") → text2_{17}
LaTeX((((("\text{\textcolor{#000099}{" * FXCV) * " = ") * valu2) * "}}")) → text2_9
LaTeX((((("\text{\textcolor{#000099}{" * FXCV) * " > ") * valu2) * "}}")) → text2_{22}
SelectedIndex(FXX_1) → FXXV_1
SelectedIndex(FXC_1) → FXCV_1
SelectedIndex(FXX_2) → FXXV_2
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}
LaTeX((((("\text{Once simplified, the equation is \textcolor{#000099}{" * FXCV_1) * " = ") * valu2_2) * "}. Because this is a false}")) → text2_{26}
LaTeX("\text{Rewrite the function \textcolor{#000099}{g(x) = 7x\; +\; 2} so that it is not in function notation.}") → text2
LaTeX((((("\text{\textcolor{#000099}{" * FXCV) * " = ") * valu1) * "\;+\; 2}")) → text2_8
LaTeX("\text{Substitute the ordered pair into the inequality \textcolor{#000099}{y > 7x\; +\; 2} and simplify.}") → text2_{14}
LaTeX((("\text{Multiply \textcolor{#000099}{7} by \textcolor{#000099}{" * FXXV) * "}.}")) → text2_{11}
LaTeX((("\text{Multiply \textcolor{#000099}{7} by \textcolor{#000099}{" * FXXV) * "}.}")) → text2_{21}
LaTeX((((("\text{\textcolor{#000099}{" * FXCV) * " > ") * valu1) * "\;+\; 2}")) → text2_{20}
LaTeX((("\text{Add \textcolor{#000099}{2} to \textcolor{#000099}{" * valu1) * "}.}")) → text2_{10}
LaTeX((("\text{Add \textcolor{#000099}{2} to \textcolor{#000099}{" * valu1) * "}.}")) → text2_{23}
LaTeX("\text{ \textcolor{#000099}{y = 7x\; +\; 2}}") → text2_4
LaTeX("\text{ \textcolor{#000099}{y = 7x\; +\; 2}}") → FormulaText["\text{ \textcolor{#000099}{y = 7x\; +\; 2}.}"]
LaTeX((((("\text{Substitute \textcolor{#000099}{" * FXXV) * "} for \textcolor{#000099}{x} and \textcolor{#000099}{") * FXCV) * "} for \textcolor{#000099}{y}.}")) → text2_7
LaTeX("\text{ \textcolor{#000099}{y > 7x\; +\; 2}}") → text2_{16}
LaTeX((((("\text{\textcolor{#000099}{(" * FXCV) * ")}\textcolor{#000099}{> 7}\textcolor{#000099}{(") * FXXV) * ")} \textcolor{#000099}{+ 2}}")) → text2_{18}
LaTeX((((("\text{Substitute \textcolor{#000099}{" * FXXV) * "} for \textcolor{#000099}{x} and \textcolor{#000099}{") * FXCV) * "} for \textcolor{#000099}{y}.}")) → text2_{19}
LaTeX((((("\text{\textcolor{#000099}{(" * FXCV) * ")}\textcolor{#000099}=\textcolor{#000099}{7}\textcolor{#000099}{(") * FXXV) * ")} \textcolor{#000099}{+ 2}}")) → text2_6
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
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
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
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}
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}
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}
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}
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}
LaTeX("\text{\mathbf{function} a relation in which every element of the domain is paired with exactly}") → text3
LaTeX("\text{one element of the range; that is, for every value of \textcolor{#000099}{x}, there is exactly one }") → text3_1
LaTeX("\text{value of \textcolor{#000099}{y}}") → text3_2
LaTeX("\text{\mathbf{inequality} a mathematical sentence that shows the relationship between }") → text3_4
LaTeX("\text{quantities that are not equivalent}") → text3_3
LaTeX("\text{Value of x:}") → DKT1
LaTeX("\text{Value of y:}") → DKT2