Question

How do you solve `y = -sqrt(x+4)` and is it a function?

Answer 1

Yes

Explanation:

Given the formula:

`y = -sqrt(x+4)`

Note that for any `x >= -4` this formula will give us a unique value for `y`.

If `x < -4` then `x+4 < 0` has no real square root (since the square of any real number is non-negative).

So the (implicit) domain of this relation is `x in [-4, oo)` and it is a function.

Another way of expressing the "unique value of `y` for each `x` in the domain" condition is to say that the graph of the relation has the vertical line property: Any vertical line will intersect with the graph of the relation at at most one point...

graph{-sqrt(x+4) [-10, 10, -5, 5]}

Answer 2

This is a function

Explanation:

There is no solving involved;
`y=-sqrt(x+4)`
is a function because for all valid values of `x` (that is `x >=-4`)
this relation generates one and only one value for `y`

You might compare this to
`y=+-sqrt(x+4)` which is not a function since two values can be generated from a single value of `x`; for example, if `x=5` then
`y=+3` and `y=-3`