Are these functions continuous and/or differentiable?

f(x) = (x+3)/(x-2); [-2,3]
f(x) = |x-3]; [-1,4]

Question

Are these functions continuous and/or differentiable?

f(x) = (x+3)/(x-2);  [-2,3]
f(x) = |x-3]; [-1,4]

anonymous · Answer

first one is not continuous or diff at x=2 and second is always cont and diff in that interval

jim_thompson5910 · Answer

|x-3| is continuous everywhere, but not differentiable at x=3

anonymous · Answer

is it abs brackets or not? if so, then jim is right

anonymous · Answer

I'm guessing the first one isn't continuous since the denominator is 0 at x=2.

I'm guessing the second one is both continuous and differentiable.

Am I correct?  By guessing, I mean "thinking".

anonymous · Answer

read what jim and i wrote.

anonymous · Answer

This is beyond ridiculous.  Anyone else experiencing issues with openstudy?  I just NOW received your messages and it caused a flashing screen.

anonymous · Answer

Lastly, why isn't it differentiable at |x-3| ?  Wouldn't it be "1"?

Thanks for the help guys!  Eased my mind a bit.

Yeah, those pipes are absolute brackets?

jim_thompson5910 · Answer

yeah the site is a bit slow or buggy at times

it's not differentiable at x = 3 because there's a corner there (ie a sharp change in slope)