对数母函数 f(x)=log x 向 g(x)=1+2·log(3x+4) 的变换演示

GeoGebra 命令及参数

1. LaTeX(steps) → counter
2. LaTeX("\text{Use the buttons below to return to the original problem or}\cr\text{randomly generate a similar practice problem.}") → RandomizationText
3. Corner(1) → A
4. Corner(3) → B
5. LaTeX((("\textcolor{#000099}{g(x)=" * g) * "}")) → Problem
6. LaTeX("\text{Identify the transformation(s) of the parent function.}") → text1
7. LaTeX("\text{Compare the domain and range of the parent function to those of the transformed}\cr\text{function }\textcolor{#000099}{g(x)}.") → text8
8. LaTeX("\text{The domain of the parent function is }\textcolor{#006633}{(0, \infty)}.") → text9
9. FractionText(((-d)) / c) → LL
10. LaTeX("\text{The transformations of }\textcolor{#006633}{f(x)}\text{ that result in }\textcolor{#000099}{g(x)}\text{ alter the rate at which the function}\cr\text{values change, but not their upper and lower bounds.}") → text12
11. LaTeX("\text{Calculate the y-intercept of }\textcolor{#000099}{g(x)}.") → text13
12. If(Defined[g(0)], LaTeX[("\approx " * g(0))], LaTeX["\text{ is undefined.}"]) → intercept
13. If(c < 0, "<", ">") → relation
14. If(c < 0, LaTeX[(("\left(-\infty," * LL) * "\right)")], LaTeX[(("\left(" * LL) * ",\infty\right)")]) → domain
15. LaTeX((((((((((("\text{Since }\textcolor{#000099}{g(x)}\text{ is a logarithmic function, the domain of }\textcolor{#000099}{g(x)}\text{ is defined by the argument}\cr\text{of the logarithmic term, }\textcolor{#000099}{" * h) * "}\text{. The condition }\textcolor{#000099}{") * h) * " > 0}\text{ or }\textcolor{#000099}{x ") * relation) * " ") * LL) * "}\text{ exists}\cr\text{on the argument. Therefore, the domain is }\textcolor{#000099}{") * domain) * "}.")) → text10
16. If(Defined[g(0)], LaTeX[(((((("\text{The y-intercept of }\textcolor{#000099}{g(x)=" * g) * "}\text{ is approximately }\textcolor{#000099}{") * g(0)) * "}\text{, or }\cr\textcolor{#000099}{(0, ") * g(0)) * ")}.")], LaTeX[(("\text{The y-intercept of }\textcolor{#000099}{g(x)=" * g) * "}\text{ is undefined.}")]) → text16
17. LaTeX((("\text{To determine how the parent function }\textcolor{#006633}{f(x) = log(x)}\text{ was transformed, compare it to }\cr\textcolor{#000099}{g(x)=" * g) * "}.")) → text2
18. LaTeX("\text{The range of both functions is }\textcolor{#000099}{(−\infty,\infty)}.") → text11
19. LaTeX("\text{Move the slider to solve the problem.}") → text0
20. LaTeX((((("\bullet \text{ The coefficient }\textcolor{#000099}{" * c) * "}\text{ is in the argument of the logarithm, }\textcolor{#000099}{") * h) * "}\text{. Multiplying}\cr\text{ the independent variable by a constant is the transformation }\textcolor{#000099}{g(x) = }\textcolor{#006633}{f(}\textcolor{#000099}{k}\textcolor{#006633}{x)}.")) → text5
21. LaTeX((((("\bullet \text{ Also notice that }\textcolor{#000099}{" * b) * "}\text{ is multiplied by }\textcolor{#000099}{") * p) * "}\text{. Multiplying the}\cr\text{ function value by a constant is the transformation }\textcolor{#000099}{g(x) = k }\textcolor{#000099}{ \cdot }\textcolor{#006633}{f(x)}.")) → text4
22. LaTeX((((("\bullet \text{ Furthermore, note the addition of }\textcolor{#000099}{" * d) * "}\text{ in the argument of the logarithm, }\textcolor{#000099}{") * h) * "}\text{.}\cr\text{ Adding a constant to the independent variable in the argument of the}\cr\text{ logarithm is the transformation }\textcolor{#000099}{g(x)=}\textcolor{#006633}{f(x}\textcolor{#000099}{+k}\textcolor{#006633}{)}.")) → text6
23. LaTeX((((("\bullet \text{ First, note that in }\textcolor{#000099}{g(x)}\text{, the constant }\textcolor{#000099}{" * a) * "}\text{ is added to }\textcolor{#000099}{") * f) * "}.\cr\text{ Adding a constant to the function value is the transformation }\textcolor{#000099}{g(x)=}\textcolor{#006633}{f(x)}\textcolor{#000099}{+k}.")) → text3
24. LaTeX("\text{Therefore, four transformations—}\textcolor{#000099}{g(x) = f(x) + k}\text{, }\textcolor{#000099}{g(x) = k \cdot f(x)}\text{, }\textcolor{#000099}{g(x) = f(kx)},\cr\text{ and }\textcolor{#000099}{g(x) = f(x + k)}\text{—have been performed on the parent function }\textcolor{#006633}{f(x) = log(x)}.") → text7
25. LaTeX("\text{The y-intercept of }\textcolor{#000099}{g(x)}\text{ is defined by the function value }\textcolor{#000099}{g(0)}\text{. Substitute }\textcolor{#000099}{0}\text{ for }\textcolor{#000099}{x}\cr\text{ and solve for }\textcolor{#000099}{g(0)}:") → text14
26. LaTeX(((((((((((((((((((" \textcolor{#000099}{g(x)=" * g) * "}\cr \textcolor{#000099}{g(0)=") * a) * "+") * b) * "log\left[") * c) * "(0)+") * d) * "\right]}\cr \textcolor{#000099}{g(0)=") * a) * "+") * b) * "log") * h(0)) * "}\cr \textcolor{#000099}{g(0) ") * intercept) * "}\cr ")) → text15