over which interval is the graph of the parent absolute value function (f(x)=|x|) decreasing?\n((-infty,infty…

over which interval is the graph of the parent absolute value function (f(x)=|x|) decreasing?\n((-infty,infty)\n(-infty,0)\n(-6,0)\n(0,infty))

over which interval is the graph of the parent absolute value function (f(x)=|x|) decreasing?\n((-infty,infty)\n(-infty,0)\n(-6,0)\n(0,infty))

Answer

Explanation:

Step1: Recall absolute - value function definition

The absolute - value function (f(x)=|x|) is defined as (f(x)=\begin{cases}x, & x\geq0\-x, & x < 0\end{cases}).

Step2: Analyze the slope for different intervals

For (x < 0), (f(x)=-x), and the slope of the line (y = -x) is (- 1<0), which means the function is decreasing. For (x\geq0), (f(x)=x), and the slope of the line (y = x) is (1>0), which means the function is increasing.

Answer:

((-\infty,0))