y= square root (x+2) is it function or no?Explain your reasoning?

Question

Y= square root (x+2),determine domain and range

Answer 1

Well now... if I wrote the function
y² = x
Then we would have a parabola extending sideways and to the right... indeed it would have two y values for every x value.

And so solving for y:
y = ±√x

This is not a function... but as you can see I specified ±, which guarantees two y-values for an x input.

In the generic equation y = √x, the root is taken to be positive by default.

This IS a function, then

The above two answerers would be right only if you assume that the square root symbol automatically means the positive and negative

Answer 2

By convention, the square root is positive. So y absolutely is a function.

Its domain is the set of all x such that x+2 has a square root -- i.e., such that x+2 is non-negative -- i.e., such that x >= -2.

As is usually the case with square roots, the range is all positive reals.

If you had been asked whether y^2 = x+2 specified a function of y, the answer would have been No. But that is NOT what you were asked.

Answer 3

y=√(x+2) is not a function because for every square root there are two possible answers: a positive one and a negative one. According to the definition of a function, every number X in the domain can only have ONE corresponding Y in the range.

For it to be a function you would need to specify which root you are using. The following examples are functions:
y=+√(x+2)
y=-√(x+2)

Answer 4

No, because y can have two values for each x ≠ -2.