Whether a function is continuous at a point

[akagami22]

Determine whether f(x) is continuous at x=2, where
f(x)= x^2 , x < 0
x, 0<= x < 2
√(x + 2), x>=2

I am not sure how to do this. Can someone please provide a little explanatory answer ?

 

[Steven G]

What are the requirements for f(x) to be continuous at x=a? You can't play the game unless you know the rules!
1a) The limit of f(x) as x approaches a from the left exists.
1b) The limit of f(x) as x approaches a from the right exists.
2) The limits from 1a and 1b must be equal.
3) f(a) must equal the common limit from 2

Verify the above for a=2

 

[HallsofIvy]

Or \(\displaystyle \lim_{x\to a} f(x)= f(a)\) since that assumes everything Jomo said.