Understanding Points of Discontinuity in Functions

[disneychannel]

What is the point of discontinuity?

ex. does x3+x/x have a point of discontinuity at x=0? if there is a discontiuity, is it it removable or not

 

[Mark44]

I'm assuming you mean (x³ + x)/x rather than x³ + (x/x).

Yes, there is a discontinuity at x = 0. The discontinuity is removable if the limit of this function as x approaches 0 exists and is finite.

 

[HallsofIvy]

Actually, the answer is the same whether it is $(x^3+ x)/x$ or $x^3+ (x/x)$.

More important than the answer is whether or not you UNDERSTAND the answer. disneychannel, do you see the difference between the functions $f(x)= (x^3+ x)/x$ and $g(x)= x^2+ 1$. What do you get when you graph each one?