Could someone please assist me with this (piecewise function):
Find the numbers at which
f(x)= {4+x^2 x less than 0}
{10+x 0

Question

Could someone please assist me with this (piecewise function):
Find the numbers at which 
f(x)= {4+x^2    x less than 0}
         {10+x    0<x and x less that or equal to 2}
         {12x^2-24x+12    2<x}
is discontinuous.

anonymous · Answer

Check the limits of the function as you reach each "endpoint" of each interval of each piece.

In other words, for instance, to see whether $f$ is discontinuous at $x=0$, find $\displaystyle\lim_{x\to0^-}f(x)$ and $\displaystyle\lim_{x\to0^+}f(x)$. If these limits do not match (not equal) then $f$ is discontinuous at $x=0$. Also, these limits must be the same as $f(0)$. 

For the first limit, $x\to0$ from the left, which translates to "consider values of $x$ to the left of $x=0$," or $x<0$. This means you use the piece of $f$ that is defined for this interval; namely $f(x)=4+x^2$.