First, lets remember the absolute value operator:
#AAc in RR# (for every element #c# in the real numbers set)
#if c>=0, abs(c) = c#
#if c<0, abs(c) = -c#
When graphing an absolute value operator, there are actually #2# graphs. Because the absolute value operation behaves in #2# different ways related to its input.
So we need to find the critical point of the absolute value. This means, we need to find the exact value of #x# where the greater values will result the output as is and the smaller values will result the output as negated.
Now it is obvious that #0# is the critical point of the absolute value operation.
To find the critical point in this problem:
#x+10=0#
#x=-10#
When #x# is greater than #-10# the input will be positive. When smaller, it will be negative.
Now we are ready to graph the line.
When #x>=-10#, #y = - (x+10) = -x - 10#
When #x<-10#, #y = - (-1) * (x+10) = x + 10#
The graph will look like this:
graph{y = - abs(x+10) [-20, 10, -5, 5]}
Why there is no positive #y#? Remember the conditions while graphing the lines. (#x>=10# and #x<-10#) When you try to plug some values of #x# you will see that there is no chance for #y# to be positive.
