Question

F(x)=1/3x-2 g(x)=3(x+2)-2what is the transformation that occurs between f(x) and G(x)

Answer 1

$f(x)=\frac{1}{3}x-2,g(x)=3(x+2)-2$

Furthermore,

$\begin{gathered} \Rightarrow g(x)=3x+6-2=3x+4 \\ \Rightarrow g(x)=3x+4 \end{gathered}$

Notice that

$\begin{gathered} 9f(x)=3x-18 \\ \Rightarrow9f(x)+22=3x+4=g(x) \\ \Rightarrow9f(x)+22=g(x) \end{gathered}$

Therefore, function g(x) is equal to function f(x) if we dilate f(x) by a factor of 9 and shift it 22 units upwards.