Continuity · Exercise 49

Consider the function shown in the figure.

Find the limit $\underset{x\to 1}{\lim }f\left(x\right)$ and determine if the following function is continuous at $x=1:$

$$fx=\{\begin{array}{cc}{x}^2+4& x\ne 1\\ 2& x=1\end{array}$$

This problem refers to a figure in its source book that isn't reproduced here.

OpenStax, Precalculus 2e · §12.3 Continuity · Exercise 49