Question

express the absolute value function f(x) = -6|x| as a piecewise - defined function.
f(x)=\begin{cases}square, & xltsquare\square, & xgeqsquareend{cases}

Explanation:

Step1: Recall absolute value definition

The absolute value function $|x|$ is defined as:

$$|x| =
LATEXBLOCK0
$$

Step2: Multiply by -6 for $x<0$

Substitute $|x|=-x$ into $f(x)=-6|x|$:
$f(x)=-6(-x)=6x$ for $x<0$

Step3: Multiply by -6 for $x\geq0$

Substitute $|x|=x$ into $f(x)=-6|x|$:
$f(x)=-6(x)=-6x$ for $x\geq0$

Answer:

$$f(x)=
LATEXBLOCK0
$$