Question

In Problems 45-60, determine whether $f$is continuous at $c$.

$$\begin{gathered} f\left(x\right)=\frac{x+3}{x-3} \\ c=3 \end{gathered}$$

Short answer

The function is not continuous

Step-by-step solution

Given information

Given function$f\left(x\right)=\frac{x+3}{x-3}$

Check whether the function is defined at c

Checking, we get

$$\begin{gathered} f\left(3\right)=\frac{3+3}{3-3} \\ f\left(3\right)=\frac{6}{0} \end{gathered}$$

It is not defined so there is no comtiniuity as there is a hole