Chapter 1.3, Problem 52E

Solution

To sketch: The graph of the piecewise function $f\left(x\right)=\left\{\begin{array}{ccc}{x}^2& \text{if}& x<-1\\ \left|x\right|& \text{if}& -1\le x<1\\ \mathrm{int}\left(x\right)& \text{if}& x\ge 1\end{array}\right.$ and given the point of discontinuity.

Given information:

  $f\left(x\right)=\left\{\begin{array}{ccc}{x}^2& \text{if}& x<-1\\ \left|x\right|& \text{if}& -1\le x<1\\ \mathrm{int}\left(x\right)& \text{if}& x\ge 1\end{array}\right.$

Concept Used:

Point of discontinuity: If a graph has undefined, break or hole at a point.

Calculation:

The graph of the piecewise-function,

  

Since there is many break points on the graph, the point of discontinuity is at all integer greater than 1.