Math Snap

STEP 1

Assumptions1. The original function is $y=\sqrt{x}$
. The transformations are applied in the following order a. Shift up9 units b. Reflect about the y-axis c. Shift left3 units

STEP 2

First, let's apply the first transformation to the original function. A shift up by9 units means we add9 to the function.
$$y = \sqrt{x} +9$$

STEP 3

Next, let's apply the second transformation. A reflection about the y-axis means we replace $x$ with $-x$ in the function.
$$y = \sqrt{-x} +9$$

STEP 4

Finally, let's apply the third transformation. A shift to the left by3 units means we replace $x$ with $(x+3)$ in the function.
$$y = \sqrt{-(x+3)} +9$$

implify the function.
$$y = \sqrt{-x-3} +9$$So, the function that is finally graphed after the transformations is $y = \sqrt{-x-3} +9$.