find the function that is finally graphed after the following transformations are applied to the graph of y=square root x in the order listed.

a. reflected about the y-axis
b. shift down 3 units
c. shifht left 9 units

please show work

-√x-5+9

Y= sqt.(-x+9) + 3

Sure! Let's go step-by-step:

a. Reflecting about the y-axis will change the sign of the x-values. So, the new equation becomes y = √(-x).

b. Shifting down 3 units will subtract 3 from the y-values. So, the new equation becomes y = √(-x) - 3.

c. Shifting left 9 units will subtract 9 from the x-values. So, the final equation becomes y = √(-(x + 9)) - 3.

Therefore, the function that is finally graphed after the transformations are applied is y = √(-(x + 9)) - 3.

To find the function after the given transformations are applied to the graph of y = sqrt(x), we can follow these steps:

Step 1: Start with the original function y = sqrt(x).

Step 2: Reflecting about the y-axis means that any point (x, y) on the original graph will become (-x, y) on the reflected graph. So, we replace x with -x in the equation: y = sqrt(-x).

Step 3: Shifting down 3 units means that we need to subtract 3 from the y-coordinates of all the points on the graph. So, we modify the equation by subtracting 3 from y: y = sqrt(-x) - 3.

Step 4: Shifting left 9 units means that we need to subtract 9 from the x-coordinates of all the points on the graph. So, we modify the equation by replacing x with (x + 9): y = sqrt(-(x + 9)) - 3.

Therefore, the function that is finally graphed after the given transformations are applied to y = sqrt(x) is:
y = sqrt(-(x + 9)) - 3.

Note: Keep in mind that these transformations are applied in the order listed. If the order were different, the final function would be different as well.