# How do you explain why f(x) = x^2 +1 is continuous at x = 2?

A graph is considered continuous between any range $\left[a , b\right]$ if you can draw it without lifting your pencil off the graph, meaning there are no holes - or locations where the value is undefined.
We can also try and take the derivative which would be $2 x$ then plug in $2$ for $x$ and get a slope of $4$. Which would mean at $x = 2$ there is a slope $4$, meaning the function exists at $2$.