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

2 Answers
Jan 13, 2018

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]}

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 >=-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#