Question

In Problems 41–44, the graph of a piecewise-defined function is given. Write a definition for each function.

Short answer

The piecewise-defined function is,

$f\left(x\right)=\left\{\begin{array}{l}10<x\le 2\\ x-1\le x\le 0\end{array}\right.$

Step-by-step solution

Step 1. Given Information 

We are given a graph of a piecewise-defined function,

Step 2. Defining the function

It can be seen from the graph that,

$f\left(x\right)=1,0<x\le 2$

The part of graph below the $x$-axis represents a line that passes through $(0,0)$.

Also for $0\le x\le 1$, the function will be,

$f\left(x\right)=x$

Step 3. Defining the function 

So, the function will be,

$f\left(x\right)=\left\{\begin{array}{l}10<x\le 2\\ x-1\le x\le 0\end{array}\right.$