Question

identify any x - values at which the absolute value function f(x)=6|x + 1|, is not continuous: x = not differentiable: x = (enter none if there are no x - values that apply; enter x - values as a comma - separated list, e.g., 1,3,5.)

Explanation:

Step1: Recall continuity property

All absolute - value functions of the form $y = a|x - h|+k$ are continuous everywhere. The function $f(x)=6|x + 1|$ is an absolute - value function. So, there are no $x$ - values at which it is not continuous.

Step2: Recall differentiability property

The general form of an absolute - value function $y = a|x - h|+k$ is not differentiable at $x=h$. For the function $f(x)=6|x + 1|$, comparing with $y = a|x - h|+k$, we have $h=-1$. So, the function is not differentiable at $x=-1$.

Answer:

not continuous: none
not differentiable: -1