Answer:
Increasing on: [tex]x\:<\:-1[/tex]
Decreasing on: [tex]x\:>\:-1[/tex]
Constant at : x=-1
Step-by-step explanation:
The given absolute value function is [tex]f(x)=|x+1|[/tex].
A function is said to be increasing if for all [tex]x_1\:>\:x_0[/tex], [tex]f(x_1)\:>\:f(x_0)[/tex]
From the graph, we can observe that the graph has a positive slope for all x-values less than -1. This implies that the interval of increase is [tex]x\:<\:-1[/tex] or [tex](-\infty,-1)[/tex]
We can also observe that, the slope of this function is negative on the interval:[tex]x\:>\:-1[/tex] or [tex](-1,\infty)[/tex].
At x=-1, the function is neither increasing nor decreasing. We say the function is constant at x=-1
