Question

express the absolute value function f(x)=7|x| as a piecewise - defined function

Explanation:

Step1: Recall absolute value definition

The absolute value function \(|x|\) is defined as \(|x|=

$$\begin{cases}x, & x\geq0\\-x, & x < 0\end{cases}$$

\).

Step2: Apply to \(f(x) = 7|x|\)

Multiply each part of the piecewise definition of \(|x|\) by 7. For \(x\geq0\), \(7|x|=7x\). For \(x < 0\), \(7|x|=7(-x)=-7x\). So the piecewise function is \(f(x)=

$$\begin{cases}7x, & x\geq0\\-7x, & x < 0\end{cases}$$

\).

Answer:

\(f(x)=

$$\begin{cases}7x, & x\geq0\\-7x, & x < 0\end{cases}$$

\)