Expert: Scott A Wilson - 9/24/2009

Question
How to explain why and correct terminology to use in explaining how to graph transition of y= sq root of x-3.  Question is: why do  we shift the transition to the right instead of the left (negative direction), what is the proper terminology to use, and  
what is the indepth explaination for this process.

Answer
It is shifted to the right since where x=3, it is like wherex=0 for the √x.
Put x=3 in the equation and it can be seen that y = √(3-3) = √0.

The proper terminology is y = √(x-3).  '√' is alt-251.
It can also be said that y = sqrt(x-3), y = squareroot(x-3), y = square root(x-3),
y = square root(x-3), y = sq root(x-3), y = sq rt(x), and maybe others.
I believe writing y = √(x-3) is the best way.  If alt-# for characters is not like,
try y = sqrt(x) or y = x^0.5.  It can also be written x^1/2.  However, note that in mathematics, powers are done first, so it should be written x^(1/2).

Again, if it were really x to the 1, divided by 2, x to the 1 would be x, and all that would be left would be to divide by 2.  In that case it would be x/2.

Note that if y = √x-3, it should be written √x - 3 to signify that the √ is applied to the x.  
Most people with questions write down √x-3 and really mean √(x-3).  That's what I've assumed,
and I haven't gotten a complaint yet in my 3,000 questions that I have been asked.

A lot of times questions must be read until the intent is understood.
Mathematically, x-y/x+y is really x - (y/x) + y, but again and again I have seen it as just
x-y/x+y and assumed it was suppose to be (x-y)/(x+y).

Fractions in books are usually written on two lines, but this is hard to do.
I could try to write that as x-y
                           -----
                            x+y,
but that most likely won't line up for you.  For me, they x-y is directly over x+y.
If expressions are to be written that way,
it is best to put all characters at the start of the line, as
x-y
-----
x+y.

I believe it is better though to remember to put in parnenthesis and put (x+y)/(x-y).

Again, I have seen many ways of expressing math, and many that aren't correct,
but I get the idea of what they mean and interpret it the way I believe they mean it.