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

1. relected about the x-axis
2. shift down 9 units
3. shift left 2 units

y=

Well, let's see. We start with y = sqrt x.

1. Reflecting about the x-axis would change the sign of y. So now we have y = -sqrt x.

2. Shifting down 9 units would mean subtracting 9 from y. So now we have y = -sqrt x - 9.

3. Shifting left 2 units would mean subtracting 2 from x. So now we have y = -sqrt(x - 2) - 9.

Putting it all together, the function after all these transformations is y = -sqrt(x - 2) - 9. Now that's a wild ride for a simple square root function!

To find the function that is finally graphed after the given transformations are applied to the graph of y = sqrt(x) in the listed order, we can apply each transformation step by step:

1. Reflecting about the x-axis: This can be achieved by taking the negative of the original function. Thus, the reflection about the x-axis gives us y = -sqrt(x).

2. Shifting down 9 units: This can be done by subtracting 9 from the original function. Therefore, the function after the shift down is y = -sqrt(x) - 9.

3. Shifting left 2 units: This can be accomplished by adding 2 to the argument of the function (inside the square root). Consequently, the final function after all the transformations is y = -sqrt(x+2) - 9.

So, the function that is finally graphed after the listed transformations are applied to y = sqrt(x) is y = -sqrt(x+2) - 9.

To find the function that is finally graphed after the given transformations are applied to the graph of y = sqrt(x), let's go through each transformation step by step.

1. Reflection about the x-axis:
To reflect a function about the x-axis, we negate the y-values. So, the reflection of y = sqrt(x) about the x-axis becomes y = -sqrt(x).

2. Shift down 9 units:
To shift a function down by a certain amount, we subtract that amount from the function. In this case, we need to shift y = -sqrt(x) down 9 units. So, the function becomes y = -sqrt(x) - 9.

3. Shift left 2 units:
To shift a function left by a certain amount, we replace x with (x + a), where 'a' is the amount of shift. In this case, we need to shift y = -sqrt(x) - 9 left 2 units. So, the function becomes y = -sqrt(x + 2) - 9.

Therefore, the function that is finally graphed after the given transformations are applied to the graph of y = sqrt(x) in the order listed is y = -sqrt(x + 2) - 9.

The answer is 3. Since the

y = -√(x+2) - 9
(-) means reflect by x-axis
-9 means 9 units down
+2 means shift left 2 units

The sign makes a difference
For shift if its negative it shift right and positive left.

1. y = -√x

2. y = -√x - 9
3. y = -√(x+2) - 9