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

Answer:

B. $(-\infty, 0)$

Explanation:

Step1: Recall absolute - value function definition

$f(x)=\begin{cases}x, & x\geq0\ -x, & x < 0\end{cases}$

Step2: Analyze the slope for $x < 0$

For $x<0$, $f(x)=-x$. The slope of $y = -x$ is $- 1<0$. So the function is decreasing on the interval $(-\infty,0)$.

Step3: Analyze the slope for $x\geq0$

For $x\geq0$, $f(x)=x$. The slope of $y = x$ is $1>0$, so the function is increasing on the interval $[0,\infty)$. Thus, the graph of $y = |x|$ is decreasing on $(-\infty,0)$.