42. Select the box or boxes that represent the transformation of each function from the parent function f(x)=x\begin{tabular}{|l|c|c|c|c|}\hline & \begin{tabular}{c} Horizontal \\Dilation\end{tabular} & \begin{tabular}{c} Vertical \\Reflection\end{tabular} & \begin{tabular}{c} Vertical \\Translation\end{tabular} & \begin{tabular}{c} Horizontal \\Translation\end{tabular} \\\hlinef(x)=∣x−2∣+2 & A & B & (C) & (D) \\\hlinef(x)=∣2x∣ & A & B & (C) & (D) \\\hlinef(x)=−∣x∣ & A & B & C & (D) \\\hlinef(x)=∣x−2∣ & A & B & C & (D) \\\hline\end{tabular}
Q. 42. Select the box or boxes that represent the transformation of each function from the parent function f(x)=x\begin{tabular}{|l|c|c|c|c|}\hline & \begin{tabular}{c} Horizontal \\Dilation\end{tabular} & \begin{tabular}{c} Vertical \\Reflection\end{tabular} & \begin{tabular}{c} Vertical \\Translation\end{tabular} & \begin{tabular}{c} Horizontal \\Translation\end{tabular} \\\hlinef(x)=∣x−2∣+2 & A & B & (C) & (D) \\\hlinef(x)=∣2x∣ & A & B & (C) & (D) \\\hlinef(x)=−∣x∣ & A & B & C & (D) \\\hlinef(x)=∣x−2∣ & A & B & C & (D) \\\hline\end{tabular}
Translate Right and Up: For f(x)=∣x−2∣+2, the function is translated 2 units to the right and 2 units up from the parent function.
Vertical Translation: Choice (C) Vertical Translation and (D) Horizontal Translation are correct for f(x)=∣x−2∣+2.
Horizontal Dilation: For f(x)=∣2x∣, the function is horizontally dilated by a factor of 21 from the parent function.
Horizontal Dilation: Choice (A) Horizontal Dilation is correct for f(x)=∣2x∣.
Vertical Reflection: For f(x)=−∣x∣, the function is reflected over the x-axis from the parent function.
Vertical Reflection: Choice (B) Vertical Reflection is correct for f(x)=−∣x∣.
Translate Right: For f(x)=∣x−2∣, the function is translated 2 units to the right from the parent function.
Horizontal Translation: Choice (D) Horizontal Translation is correct for f(x)=∣x−2∣.