Chapter 3.8, Problem 44PPS

To determine

To write: the given absolute function as piecewise function.

Explanation of Solution

Given information:

The function $f(x)=2\left|x\right|+1$

The graph of the function $f(x)=2\left|x\right|+1$

The value of the absolute function is always positive or equal to zero.

Consider the function $f(x)=\left|x\right|=\{\begin{array}{l}-x;x<0\\ x;x\ge 1\end{array}$

The function $f(x)=2\left|x\right|+1$

  $=\{\begin{array}{l}-2x+1;x<0\\ \text{2x+1 };x\ge 0\end{array}$

Hence, the piecewise function of $f(x)=2\left|x\right|+1=\{\begin{array}{l}-2x+1;x<0\\ 2x+1;x\ge 0\end{array}$.