Compare the graph of the following function with the graph of $f ( x ) = \sqrt { x }$. $y = \sqrt { - x + 4 }$
A) First a vertical shift of 4 units up then a reflection in the $y$-axis.
B) First a horizontal shift of 4 units to the left then a reflection in the $y$-axis.
C) First a vertical shift of 4 units up then a reflection in the $x$-axis.
D) First a horizontal shift of 4 units to the left, then a vertical shift of 4 units up and then a reflection in the $y$-axis.
E) First a horizontal shift of 4 units to the left then a reflection in the $x$-axis.

Question

Quizplus · Accepted Answer

The correct transformation sequence for $y = \sqrt{-x + 4}$ compared to $f(x) = \sqrt{x}$ is a horizontal shift of 4 units to the right (not left, as the inside of the square root becomes $x - 4$ when you factor out the negative, indicating a right shift) and then a reflection in the $y$-axis (due to the negative sign in front of $x$, which flips the graph over the $y$-axis). The choice provided in the question contains a mistake in the direction of the shift, but the closest correct process given the options is B, acknowledging an error in the explanation regarding the direction of the shift.

Compare the Graph of the Following Function with the Graph f(x)=xf ( x ) = \sqrt { x }f(x)=x​

Compare the Graph of the Following Function with the Graph $f ( x ) = \sqrt { x }$