Chapter 1.3, Problem 46E

Solution

To sketch: The graph of the piecewise function $f\left(x\right)=\left\{\begin{array}{cc}{x}^3& \begin{array}{cc}\text{if}& x\le 0\end{array}\\ e^x& \begin{array}{cc}\text{if}& x>0\end{array}\end{array}\right.$ and given the point of discontinuity.

Given information:

  $f\left(x\right)=\left\{\begin{array}{cc}{x}^3& \begin{array}{cc}\text{if}& x\le 0\end{array}\\ e^x& \begin{array}{cc}\text{if}& x>0\end{array}\end{array}\right.$

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 a break point on the graph, the point of discontinuity is at $x=0$ .