Q. 42 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

The piecewise-defined function is, 

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

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, 

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