Find the function.
-Find the function that is finally graphed after the following transformations are applied to the graph of y =x. The graph is shifted up 4 units, reflected about the y-axis, and finally shifted left 3 units.
A) $y = - \sqrt { x + 3 } + 4$
B) $y = \sqrt { - x + 3 } - 4$
C) $y = \sqrt { - x - 3 } + 4$
D) $y = \sqrt { - x - 3 } - 4$

Question

Find the function.
-Find the function that is finally graphed after the following transformations are applied to the graph of y =x. The graph is shifted up 4 units, reflected about the y-axis, and finally shifted left 3 units. 
A) $y = - \sqrt { x + 3 } + 4$
B) $y = \sqrt { - x + 3 } - 4$
C) $y = \sqrt { - x - 3 } + 4$
D) $y = \sqrt { - x - 3 } - 4$

Quizplus · Accepted Answer

The correct transformations applied to $y = \sqrt{x}$ to achieve the described final graph are: shifting up 4 units, reflecting about the y-axis (which changes $x$ to $-x$), and shifting left 3 units (which adds 3 inside the square root, resulting in $\sqrt{-x-3}$). Adding 4 to account for the upward shift gives the final function $y = \sqrt{-x-3} + 4$.

Find the Function y=−x+3+4y = - \sqrt { x + 3 } + 4y=−x+3​+4

Find the Function $y = - \sqrt { x + 3 } + 4$