over which interval is the graph of the parent absolute value function $f(x)=|x|$ decreasing?\n$(-\\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|) can be written as (f(x)=\begin{cases}x, & x\geq0\-x, & x < 0\end{cases}).

Step2: Analyze the slope for different intervals

For (x\geq0), (f(x)=x), and the slope (m = 1) (function is increasing). For (x<0), (f(x)=-x), and the slope (m=- 1) (function is decreasing).

Answer:

((-\infty,0))