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

Jan 13, 2018

Yes

#### Explanation:

Given the formula:

$y = - \sqrt{x + 4}$

Note that for any $x \ge - 4$ 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 $x \in \left[- 4 , \infty\right)$ 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]}

Jan 13, 2018

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 $x \ge - 4$)
this relation generates one and only one value for $y$

You might compare this to
$y = \pm \sqrt{x + 4}$ 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 $y = - 3$