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 4 units to the right (not left, as the inside of the square root becomes zero at $x=4$, indicating a rightward shift), followed by a reflection in the $y$-axis due to the negative sign in front of $x$. This is because the negative sign in front of $x$ flips the graph over the $y$-axis, and adding 4 inside the square root shifts the graph to the right, not left as initially stated. The correct description should indicate a rightward shift, not leftward, making the initial choice incorrect based on the standard interpretation of function transformations.

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 $f ( x ) = \sqrt { x }$