Chapter 1, Problem 19RE

Solution

To draw the graph of the given function and find whether the function is continuous at $x=0$ or not.

Yes, the function $f(x)=\frac{x^2-3}{x+2}$ is continuous at $x=0$ .

Given :  The given function is:

  $f(x)=\frac{x^2-3}{x+2}$

Graph: The graph of the function is plotted below:

  

Interpretation: Graphly, a function is said to be continuous at a point if the graph does not break at the point. Here, from the above graph, the function is defined at $x=0$ and all its nearby points. And the function does not come apart at $x=0$ . Hence, the function $f(x)=\frac{x^2-3}{x+2}$ is continuous at $x=0$ .