Q:

Determine the intervals on which the function is increasing, decreasing, and constant. An absolute value function is shown facing down with a vertex of -1,0.

Accepted Solution

A:
Answer:Increasing on: [tex]x\:<\:-1[/tex]Decreasing on: [tex]x\:>\:-1[/tex]Constant at : x=-1Step-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