Is the function attached inside continuous for all of x?

**answer choices attached inside too :)

please explain!! thanks!!

Question

Is the function attached inside continuous for all of x?

**answer choices attached inside too :)

please explain!! thanks!!

anonymous · Answer

function:)

anonymous · Answer

answer choices A,B,C,D,E from top to bottom!! :)

mertsj · Answer

If you look at the graph of this function you will probably be able to answer the question: http://www.wolframalpha.com/input/?i=plot%3A++y%3D |x|%2Fx

anonymous · Answer

would it be answer choice A or C? 

that's what i have it narrowed down to right now

mertsj · Answer

It can't be a because the function is defined for x = 0

luigi0210 · Answer

Well, if you take the limit: 
$$\LARGE \lim_{x \rightarrow 0^-} f(x)=-1$$
$$\LARGE \lim_{x \rightarrow 0^+} f(x)=1$$
and then that 0.

mertsj · Answer

c is good because the limit does not exist.

mertsj · Answer

d and e won't work because it is not continuous

luigi0210 · Answer

^Pretty much. 3 different values for the same x.

anonymous · Answer

ohh okay i see :)

thanks so much!! @Luigi0210 @Mertsj :)

mertsj · Answer

yw