Piece-Wise Function Continuity

[justapinkday]

Homework Statement

Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold.

f(x)= {x^3 if x < or = -2
{2 if x > -2

Homework Equations

The conditions are that a function is said to be continuous at x=c if the following conditions hold:
1 f(c) exists
2 lim as x approaches c f(x) exists
3 lim as x approaches c f(x) = f(c)

The Attempt at a Solution

My professor has not explained this and has assigned it...no clue what to do!

 

[micromass]

You will have to calculate the limit in each point and see whether the left and right sided limits are equal.