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

1 Answer
Jun 21, 2016

Answer:

There is no 'hole' in the graph and you can find the derivative at x =2.

Explanation:

A graph is considered continuous between any range #[a, b]# 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 #2x# 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#.