square root funcation clarification

[M-D]

Hi,

I just had one thing bothering me regarding the square root function which i wanted to clarify.

For a function like the graph will be translated two units to the right and one unit up. Hence, you must take the opposite of which would be and thus transate the graph 2 units right. the end point is therefore

However, if the function is this graph still has an end point of which means that you don't take the opposite of the sign in this case i.e. doesn't become when thinking about transformations.

Is this difference because if is factored out then the equation will become and thus you do end up taking the opposite of the sign of the two i.e. is seen as for the transformation?

Thanks in advance for any help

[brightsky]

you are spot on! y = sqrt(2-x) + 1, in transformation form, looks like y = sqrt(-(x-2)) + 1, so to get from y = sqrt(x) to y = sqrt(2-x) + 1, you need to perform the following sequence of transformations:

1. reflect in the y-axis
2. translate 2 units in the POSITIVE direction of the x-axis
3. translate 1 unit in the positive direction of the y-axis

hence the end point is at (2,1).