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

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

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

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

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

Answer:

B. ((-\infty,0))