Sketch a possible function on the domain (−2 , 4) that is : Not differentiable only at x=(−1.5), (−1), 0, 0.5, 1, 3, not continuous only at x=(−1), 0.5, 3 and has no limit only at x=0.5, 3.

I'm confused how it is suppose not be continuous at -1 but still have a limit at -1,

Can someone possibly graph this?

Question

Sketch a possible function on the domain (−2 , 4) that is : Not differentiable only at x=(−1.5), (−1), 0, 0.5, 1, 3, not continuous only at x=(−1), 0.5, 3 and has no  limit only at x=0.5, 3.

I'm confused how it is suppose not be continuous at -1 but still have a limit at -1, 

Can someone possibly graph this?

accessdenied · Answer

maybe there is just a hole in the graph at x = -1

i believe if the limit exists approaching from both sides and they are equal, then that would be the limit at the point, even though the point itself isn't there

holes in the graph appear when you have a factor in the denominator that makes the denominator zero, and also the same in the numerator.

(x + 1)
------     
(x + 1)

would be one case.  (when x = -1, a hole just appears, but otherwise its a standard y = 1  graph)

accessdenied · Answer

ill have to double check on this, its been a while  lol

anonymous · Answer

so would it be like a hollow circle or just a straight up break in the line?

accessdenied · Answer

|dw:1329962219896:dw|

like that