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.
