pre-calc functions question

[TheSeeker03]

A square root of a positive number always has two answers. Same absolute value, but one number is positive, the other negative.

SQRT(16) = +4 and also -4

So why then is y(x)=SQRT(x) a function (i.e. passes vertical line test).

When I graph it in my calculator it graphs only the positive half of a porabola.

[jay_shark]

f(x)^2=x is not a function since f(x)=+-sqrtx .

However , F(x)=+sqrtx is a function .

Similarly x^2+y^2=1 is not a function but if we take the top hemisphere and exclude the bottom then it becomes a function .

y=+sqrt(1-x^2)

[BruceZ]

[ QUOTE ]
A square root of a positive number always has two answers. Same absolute value, but one number is positive, the other negative.

SQRT(16) = +4 and also -4

So why then is y(x)=SQRT(x) a function (i.e. passes vertical line test).

When I graph it in my calculator it graphs only the positive half of a porabola.

[/ QUOTE ]

When you use the radical sign to denote the square root, that is defined to be the principal square root, which is positive. When we wish to specify the negative square root, we precede the radical sign with a minus sign. For example, the quadratic formula is written

[-b +/- sqrt(b^2 - 4ac)]/2a

The +/- is necessary since otherwise the sqrt would only specify the positive value.