Chapter 1.3, Problem 47E

Solution

To sketch: The graph of the piecewise function $f\left(x\right)=\left\{\begin{array}{cc}\left|x\right|& \begin{array}{cc}\text{if}& x<0\end{array}\\ \sin x& \begin{array}{cc}\text{if}& x\ge 0\end{array}\end{array}\right.$ and given the point of discontinuity.

Given information:

  $f\left(x\right)=\left\{\begin{array}{cc}\left|x\right|& \begin{array}{cc}\text{if}& x<0\end{array}\\ \sin x& \begin{array}{cc}\text{if}& x\ge 0\end{array}\end{array}\right.$

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 no any break point or hole on the graph, there is not any point of discontinuity.