Let’s take a look at what this function looks like when graphed, so we can better understand the nature of the domain. If you graph y=|x+1|, you will end up with a “V”
We can see that the domain of this function is all real numbers, as the function is defined over all real numbers.
Now, let’s examine the behavior of the function in this domain. We see that the function is increasing over certain regions of the domain. Specifically, the function is increasing when x is less than -1 and when x is greater than -1. This can be seen clearly in the graph, as the “V” shape shows that the function increases on either side of the point where x=-1.
So, to summarize, we can say that the domain of the function y=|x+1| is all real numbers, and that within this domain, the function is increasing when x is less than -1 and greater than -1.