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Select the box or boxes that represent the transformation of each function from the parent function 
f(x)=x









Horizontal


Dilation







Vertical


Reflection







Vertical


Translation







Horizontal


Translation







f(x)=|x-2|+2
A
B
(C)
(D)



f(x)=|2x|
A
B
(C)
(D)



f(x)=-|x|
A
B
C
(D)



f(x)=|x-2|
A
B
C
(D)

4242. Select the box or boxes that represent the transformation of each function from the parent function f(x)=x f(x)=x \newline\begin{tabular}{|l|c|c|c|c|}\newline\hline & \begin{tabular}{c} \newlineHorizontal \\\newlineDilation\newline\end{tabular} & \begin{tabular}{c} \newlineVertical \\\newlineReflection\newline\end{tabular} & \begin{tabular}{c} \newlineVertical \\\newlineTranslation\newline\end{tabular} & \begin{tabular}{c} \newlineHorizontal \\\newlineTranslation\newline\end{tabular} \\\newline\hlinef(x)=x2+2 f(x)=|x-2|+2 & A & B & (C) & (D) \\\newline\hlinef(x)=2x f(x)=|2 x| & A & B & (C) & (D) \\\newline\hlinef(x)=x f(x)=-|x| & A & B & C & (D) \\\newline\hlinef(x)=x2 f(x)=|x-2| & A & B & C & (D) \\\newline\hline\newline\end{tabular}

Full solution

Q. 4242. Select the box or boxes that represent the transformation of each function from the parent function f(x)=x f(x)=x \newline\begin{tabular}{|l|c|c|c|c|}\newline\hline & \begin{tabular}{c} \newlineHorizontal \\\newlineDilation\newline\end{tabular} & \begin{tabular}{c} \newlineVertical \\\newlineReflection\newline\end{tabular} & \begin{tabular}{c} \newlineVertical \\\newlineTranslation\newline\end{tabular} & \begin{tabular}{c} \newlineHorizontal \\\newlineTranslation\newline\end{tabular} \\\newline\hlinef(x)=x2+2 f(x)=|x-2|+2 & A & B & (C) & (D) \\\newline\hlinef(x)=2x f(x)=|2 x| & A & B & (C) & (D) \\\newline\hlinef(x)=x f(x)=-|x| & A & B & C & (D) \\\newline\hlinef(x)=x2 f(x)=|x-2| & A & B & C & (D) \\\newline\hline\newline\end{tabular}
  1. Translate Right and Up: For f(x)=x2+2f(x)=|x-2|+2, the function is translated 22 units to the right and 22 units up from the parent function.
  2. Vertical Translation: Choice (C) Vertical Translation and (D) Horizontal Translation are correct for f(x)=x2+2f(x)=|x-2|+2.
  3. Horizontal Dilation: For f(x)=2xf(x)=|2x|, the function is horizontally dilated by a factor of 12\frac{1}{2} from the parent function.
  4. Horizontal Dilation: Choice (A) Horizontal Dilation is correct for f(x)=2xf(x)=|2x|.
  5. Vertical Reflection: For f(x)=xf(x)=-|x|, the function is reflected over the xx-axis from the parent function.
  6. Vertical Reflection: Choice (B) Vertical Reflection is correct for f(x)=xf(x)=-|x|.
  7. Translate Right: For f(x)=x2f(x)=|x-2|, the function is translated 22 units to the right from the parent function.
  8. Horizontal Translation: Choice (D) Horizontal Translation is correct for f(x)=x2f(x)=|x-2|.

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